Question

The roots of a quadratic equation are 4 and -5. Which quadratic equation has these roots?

Answer 1

(x-4)(x+5) or x^2+x-20

Explanation:

If a root of the function is 4, (meaning that when y=0, x=4) it can be rewritten as x-4.

The same goes for if a root is -5. it will simplify to x+5.

These are called factors of a quadratic equation.

Put together, they look like (x-4)(x+5). Using the FOIL method, that can be simplified to x^2+x-20

Answer 2

Standard Form:
`y = x^2 + x - 20`

Factored Form:
`y = 1(x -4)(x +5)`

Explanation:

Hello!

We can utilize the factored form of a quadratic to find the equation.

Factored Form of a Quadratic:
`y = a(x -h)(x - k)`

• h and k are the roots

We simply plug in the values of the roots and expand to find the equation. Replace "a" with 1.

Expand

• 
  `y = a(x +h)(x + k)`
• 
  `y = 1(x -4)(x +5)`
• 
  `y = 1(x^2 + x - 20)`
• 
  `y = x^2 +x - 20`

The quadratic equation
`y = x^2 + x - 20` has the roots 4 and -5.