Question

Use the graph f(x) = -x² +8x+20 to determine the values of :

2.2.1 p for which -x² +8x+p=0 will have equal roots.​

Answer 1

Answer: We want to find the value of p for which the quadratic equation -x² + 8x + p = 0 has equal roots.

For a quadratic equation ax² + bx + c = 0 to have equal roots, the discriminant b² - 4ac must be equal to 0.

In this case, the quadratic equation is -x² + 8x + p = 0, so we have a = -1, b = 8, and c = p.

Therefore, we have:

b² - 4ac = 8² - 4(-1)(p)

= 64 + 4p

For the equation to have equal roots, the discriminant must be equal to 0, so:

64 + 4p = 0

4p = -64

p = -16

So, the value of p for which the quadratic equation -x² + 8x + p = 0 has equal roots is -16.

Explanation: