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

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

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`