https://padlet.com/lglover3/pzfva2ygvdcy Made with a stroke of good luck en-us 2017-02-27 14:44:10 UTC 2017-02-27 17:48:29 UTC hello@padlet.com lglover3 https://padlet.com/lglover3/pzfva2ygvdcy/wish/156420071 We have recently been introduced to the the following terms in relation to solving a quadratic equation:
- imaginary number (i),
- complex numbers, 
- discriminant 

Complete a search on these words and compose a brief description providing the definition of these terms in your own words to briefly describe how you would solve a quadratic equation involving an imaginary number. Explain why the solution to a quadratic equation that involves a negative number under the radical would be consider to be a solution that is not a real number but a complex solution (number). Use the internet or video on YouTube to assist you. You will need to provide an example with the solution to support your reasoning.]]> 2017-02-27 14:44:38 UTC https://padlet.com/lglover3/pzfva2ygvdcy/wish/156420071 https://padlet.com/lglover3/pzfva2ygvdcy/wish/156451541 Imaginary number-  a number that when inside the radical is represented as negative, and when squared remains a negative result.
http://www.mathsisfun.com/definitions/imaginary-numbers.html

Complex Numbers- A real and an imaginary number represented and combined in a mathematical equation.
https://www.mathsisfun.com/definitions/complex-number.html

Discriminant- This number gives an idea of how many roots are involved in the solution (1,2, or 0), as well as the nature of them.
http://www.icoachmath.com/math_dictionary/discriminant.html

When solving for the roots in a quadratic function, the discriminant is the number that will help you do so. The equation b^2-4ac, is what is used to solve for the roots (b being the discriminant). When knowing how to recognize an imaginary number, just look to see if the number under the radical is that of a negative. If so, this number is imaginary because there are not two of the same number and value that will give you a negative number as a result when squared. If in the equation there is also a real number involved (10), then this becomes a complex solution (number). It would look something like this: 10-7i (i representing imaginary). When tying all these pieces together, the imaginary number tells you something about the final solution. It tell you that there are to roots involved in this quadratic function. Technically, this means there is no solution to the problem, as you can not find the x intercepts when an imaginary number is under the radical.


]]> 2017-02-27 15:52:37 UTC https://padlet.com/lglover3/pzfva2ygvdcy/wish/156451541 https://padlet.com/lglover3/pzfva2ygvdcy/wish/156451766 Imaginary Number: It is a complex number that can be written as a real number when it is multiplied by the imaginary unit i. Keep in mind that i^2 = -1. For example, if you have 5i, then its square is -25 (link here). If there is a negative in an equation (and it is under a radical), then there will be an imaginary number in the result (as seen with the equation above – the square root of -25 = 5i).

Complex Number: A complex number can be expressed in the form a + bi where a and b are real numbers and i is the imaginary unit (link here).
Examples: 2 + 3i (where a=2 and b=3) or 3i (where b=3).

Discriminant:  The discriminant reveals what type of roots an equation has. The form of the discriminant in the quadratic equation takes the form of b^2 - 4ac (link here). For example, when the discriminant is a negative number, then there will be no real solutions (meaning there will be no x-intercepts).]]> 2017-02-27 15:53:08 UTC https://padlet.com/lglover3/pzfva2ygvdcy/wish/156451766 https://padlet.com/lglover3/pzfva2ygvdcy/wish/156451779 Imaginary number: an imaginary number is a number that when squared, it is equal to a negative ex: i^2=-1 (i=imaginary number) (http://www.mathsisfun.com/numbers/imaginary-numbers.html)

Complex number: a combination of a real number and an imaginary number
ex: 1+i , 39+2i (https://www.mathsisfun.com/numbers/complex-numbers.html)

Discriminant: b^2 - 4ac
Ex: 2^2-4(5)(2)
they are coefficients of a polynomial equation whose value gives information about the roots (x-intercepts) of the polynomial (https://www.mathsisfun.com/algebra/quadratic-equation.html)

The discriminant is used in relation to the quadratic formula by helping find the x intercepts (roots). Imaginary numbers are helpful in a quadratic equation because if there is a negative number under the radical, there is no x- intercepts. I know this because no numbers multiplied together can equal a negative. Complex numbers are used to solve when there is an imaginary number in the quadratic equation. For example, 6=/- the square root of -65 divided by 2. this would then later simplify to 3+4i. 

]]> 2017-02-27 15:53:09 UTC https://padlet.com/lglover3/pzfva2ygvdcy/wish/156451779 https://padlet.com/lglover3/pzfva2ygvdcy/wish/156451875 Imaginary Numbers:
Imaginary numbers are the result of  finding the square root of a negative numbers. You can't multiply a negative number by itself and still get a negative number, but with imaginary numbers that it what happens. With imaginary numbers in quadratic equations, there will be no x - intercepts because you cannot find a number for the square root of a negative....
Complex numbers:
A complex number is the combination of an imaginary number and a real number. You multiply a real number....
http://www.purplemath.com/modules/complex3.htm
https://www.mathsisfun.com/definitions/complex-number.html
Discriminant:
The discriminant of the quadratic formula determines the roots of an equation...... http://www.mathwords.com/d/discriminant_quadratic.htm

]]> 2017-02-27 15:53:24 UTC https://padlet.com/lglover3/pzfva2ygvdcy/wish/156451875 https://padlet.com/lglover3/pzfva2ygvdcy/wish/156451914 Imaginary Number- This number is the result of finding the square root of a negative. This occurs whens solving quadratic equations because the degree of the equation is 2. This means that in solving, square roots will be solved for and if there are negatives in the equation, at least one imaginary number will be in the result.
Example: square root of -4
https://www.mathsisfun.com/numbers/imaginary-numbers.html

Complex Numbers- A complex number is the result of multiplying an imaginary number to a real number and then adding another real number.
Example:  3 times the square root of -4 +5
https://www.mathsisfun.com/numbers/complex-numbers.html

Discriminant- The discriminant of a quadratic equation is what determines how many roots the visual representation will have. In other words- it determines how many times the function hit the x-axis
example: 3 squared minus 4 times 2 times
https://www.mathsisfun.com/algebra/quadratic-equation.html]]> 2017-02-27 15:53:29 UTC https://padlet.com/lglover3/pzfva2ygvdcy/wish/156451914 https://padlet.com/lglover3/pzfva2ygvdcy/wish/156451973 An imaginary number is a number that is shown by the square root of a negative number . A number represented by i.  A complex number is a number that can be represented in the form a +bi, where a and b are real numbers and i is the imaginary unit. i² = -1.  The discriminant is a function of the coefficient in an equation which is a polynomial and it gives information about the square roots of the polynomial.  When solving a quadratic equation with an imaginary number you must consider that the square of an imaginary number bi is −b² .  When a quadratic equation has an imaginary number on the bottom you know there are no roots because there cant be a negative number on the bottom of the quadratic equation. For example: b² - 4ac. 2² - 4(1)(3)
4-12=-8. The negative square root means the number is an imaginary number and therefore does says there are no rots for the equation.
http://www.mathcentre.ac.uk/resources/sigma%20complex%20number%20leaflets/sigma-complex2-2009-1.pdf]]> 2017-02-27 15:53:36 UTC https://padlet.com/lglover3/pzfva2ygvdcy/wish/156451973 https://padlet.com/lglover3/pzfva2ygvdcy/wish/156452321 Since there can't be a negative number underneath a radical sign i is replacing the negative one that is multiplied by the positive number underneath the radical sign.
Imaginary numbers- when squared gives a negative result.

ex: i is replaced with the radical of -1
i^2=-1
https://mathbitsnotebook.com/Algebra1/Radicals/RADNegativeUnder.html
Complex numbers- a number that is expressed as an imaginary number and a real number
-36 (under the radical)
= i6
Discriminant- The solution to the equation underneath the radical (b^2 -4ac). For example a positive  perfect square the out come is two 
discriminant shows that the quadratic has two rational solutions. A negative discriminant shows that there are no roots because of the imaginary number. Positive non per

]]> 2017-02-27 15:54:31 UTC https://padlet.com/lglover3/pzfva2ygvdcy/wish/156452321 https://padlet.com/lglover3/pzfva2ygvdcy/wish/156452901 Complex numbers- numbers that can be expressed using both imaginary and real numbers. For example, the radical of -4 --> 2i.
https://en.wikipedia.org/wiki/Complex_number

discriminant- In the quadratic formula, the discriminant is the group of numbers underneath the radical. When you have a positive, perfect square discriminant, the outcome is two rational solutions. When you have a positive non perfect square discriminant, the outcome is two irrational solutions. When you have a negative discriminant of any kind, which includes the imaginary number "i", the outcome is no solutions. https://www.khanacademy.org/math/algebra/quadratics/solving-quadratics-using-the-quadratic-formula/a/discriminant-review

imaginary numbers-  numbers that replace real numbers that create in error in the specific equation it is in. For example, if you have a negative in a radical it comes out as an error so to fix that the radical of -1 in which the number is multiplied by is replaced with the imaginary number i. There for the equation becomes i multiplied by the radical of x.  https://en.wikipedia.org/wiki/Imaginary_number]]> 2017-02-27 15:55:34 UTC https://padlet.com/lglover3/pzfva2ygvdcy/wish/156452901 https://padlet.com/lglover3/pzfva2ygvdcy/wish/156453720 Imaginary Number -- An imaginary number is a number that when  squared, you get a negative number as the result. Example: 3i, or -4.2i. ("i" means to multiply by the square root of -1).

Complex Number -- A complex number is the combination of an imaginary number and real number. Example: 2 + i, or 22 + 4i

Discriminant -- The discriminant is what tells us how many roots are in the given quadratic equation.
http://www.mathsisfun.com

The discriminant in a quadratic equation is the number that tells you where the equation hits on the x-axis. In some quadratic equations there is a negative sign beneath the radical meaning that it is an imaginary number. From this point you know that there are no x-intercepts (roots) in this equation, because of the imaginary number in the equation...]]> 2017-02-27 15:57:26 UTC https://padlet.com/lglover3/pzfva2ygvdcy/wish/156453720 https://padlet.com/lglover3/pzfva2ygvdcy/wish/156453969 The backbone of imaginary numbers is the imaginary unit i. One can create more pure imaginary by taking multiples of i. A complex number is a number that can be written in the form A+Bi, where A is the real part and Bi is the imaginary part. An example of a complex number is 4+6i. The discriminant is the part of the quadratic equation that is under the square root sign (radical), which will find you the roots of a parabola. This is connected to imaginary and complex numbers as, if one has a negative number under the radical in the quadratic equation (or a negative discriminant) then it will be an imaginary number.  For example if one has the number -4 as the discriminant, it can be rewritten as i radical 2. This means one has to use their previous knowledge of simplifying radicals and imaginary numbers to solve equations that has a negative discriminant. ]]> 2017-02-27 15:58:01 UTC https://padlet.com/lglover3/pzfva2ygvdcy/wish/156453969 https://padlet.com/lglover3/pzfva2ygvdcy/wish/156456781 An Imaginary number occurs when finding the square root of a negative number/ when a negative number is under the radical, or a number that when squared is equal to a negative. A complex number is a combination of an imaginary number and a real number. The discriminant tells you about how many roots there are and the nature of the number.

When there is an imaginary number in quadratic formula you know that there is no x-intercept because you cant find a number that is the square root of a negative number...

]]> 2017-02-27 16:04:12 UTC https://padlet.com/lglover3/pzfva2ygvdcy/wish/156456781