Question

Write the quadratic equation whose roots are -3 and 4 and whose leading coefficient is 4

Answer 1

`4x^2 -4x - 48 = 0`

Explanation:

Given

`x= -3 \ or\ 4` -- roots

`n= 4` --- leading coefficient

Required

Calculate the quadratic equation

`x= -3 \ or\ 4`

Split to 2:

`x = -3\ or\ x = 4`

Equate both to 0

`x +3 = 0\ or\ x - 4= 0`

Multiply both together:

`(x + 3) * (x - 4) = 0 * 0`

`(x + 3) * (x - 4) = 0`

`x^2 -4x +3x - 12 = 0`

`x^2 -x - 12 = 0`

Multiply both sides by the leading coefficient, n

`n * [x^2 -x - 12] = 0 * n`

`4 * [x^2 -x - 12] = 0 * 4`

`4 * [x^2 -x - 12] = 0`

Open brackets

`4x^2 -4x - 48 = 0`