What is the discriminant of -x^2+10x-56=-4x-7−x2+10x−56=−4x−7?

1 Answer
Stefan V.
Jul 27, 2015

For this quadratic, Delta = 0.

Explanation:

In order to determine the determinant of this quadratic equation, you must first get it to quadratic form, which is

ax^2 + bx + c = 0

For this general form, the determinant is equal to

Delta = b^2 - 4 * a * c

So, to get your equation to mthis form, add 4x + 7 to both sides of the equation

-x^2 + 10x - 56 + (4x + 7) = -color(red)(cancel(color(black)(4x))) - color(red)(cancel(color(black)(-7))) + color(red)(cancel(color(black)(4x))) + color(red)(cancel(color(black)(7)))

-x^2 + 14x - 49 = 0

Now identify what the values for a, b, and c are. In your case,

{(a = -1), (b=14), (c=-49) :}

This means that the discriminant will be equal to

Delta = 14^2 - 4 * (-1) * (-49)

Delta = 196 - 196 = color(green)(0)

This means that your equation has only one real root

x_(1,2) = (-b +- sqrt(Delta))/(2a)

x = (-b +- sqrt(0))/(2a) = color(blue)(-b/(2a))

In your case, this solution is

x = (-14)/(2 * (-1)) = 7

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