What is the discriminant of $m^2-8m=-14$ and what does that mean?

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Answer 1 · 2018-06-17T13:06:36

See a solution process below:

First, put the equation in standard quadratic form:

$m^2 - 8m = -14$

$m^2 - 8m + color(red)(14) = -14 + color(red)(14)$

$m^2 - 8m + 14 = 0$

or

$1m^2 - 8m + 14 = 0$

For $ax^2 + bx + c = 0$ , the values of $x$ which are the solutions to the equation are given by:

$x = (-b +- sqrt(b^2 - 4ac))/(2a)$

The discriminate is the portion of the quadratic equation within the radical: $color(blue)(b)^2 - 4color(red)(a)color(green)(c)$

If the discriminate is:
- Positive, you will get two real solutions
- Zero you get just ONE solution
- Negative you get complex solutions

To find the discriminant for this problem substitute:

$color(red)(1)$ for $color(red)(a)$

$color(blue)(-8)$ for $color(blue)(b)$

$color(green)(14)$ for $color(green)(c)$

$color(blue)(-8)^2 - (4 * color(red)(1) * color(green)(14)) =>$

$64 - 56 =>$

$8$

Because the discriminate is Positive, you will get two real solutions.

What is the discriminant of m^2-8m=-14m^2-8m=-14 and what does that mean?