Question

Select the quadratic that has roots x=8 and x=-5

Answer 1

We know that x = 8 and x = -5, thus

$\bf \begin{cases} x=8\implies &x-8=0\\ x=-5\implies &x+5=0 \end{cases} \\\\\\ (x-8)(x+5)=\stackrel{original~polynomial}{y}\implies x^2-3x-40=y$

Answer 2

Answer:

Quadratic equation: $x^2-3x-40=0$

Step-by-step explanation:

We are given two roots of the quadratic equation and we need to find the quadratic equation.

If roots are a and b then equation

$x^2-(\text{sum of roots})x+\text{Product of root}=0$

Roots are x=8 and x=-5

Sum of roots  = 8 + (- 5) = 3

Product of roots = 8 x -5 = -40

Substitute the value into formula

Quadratic equation:

$x^2-3x-40=0$

In factor form:

$(x-8)(x+5)=0$

Hence, The equation is  $x^2-3x-40=0$