Question

use the graph f(x)=-x²+8x+20 to determine the values of: p for which -x²+8x+p=0 will have equal roots​

Answer 1

According to the discriminant of the quadratic equation, it will have equal roots for p = -16.

What is the discriminant of a quadratic equation and how does it influence the solutions?

A quadratic equation is modeled by:

$y = ax^2 + bx + c$

The discriminant is:

$\Delta = b^2 - 4ac$

The solutions are as follows:

• If $\mathbf{\Delta > 0}$, and it is a perfect square, it has 2 rational solutions.

• If $\mathbf{\Delta > 0}$, and it is not a perfect square, it has 2 irrational solutions.

• If $\mathbf{\Delta = 0}$, it has equal roots.

• If $\mathbf{\Delta < 0}$, it has 2 complex solutions.

In this problem, the equation is:

$f(x) = -x^2 + 8x + p$

Hence the coefficients are a = -1, b = 8, c = p.

It has equal roots if $\Delta = 0$, hence:

$b^2 - 4ac = 0$

$8^2 + 4p = 0$

$4p = -64$

$p = -16$

More can be learned about the discriminant of a quadratic equation at https://brainly.com/question/19776811