Question

Write the quadratic equation whose roots are 5 and -6, And whose leading coefficient is 3

Answer 1

3
`x^(2)`-9x-90

Explanation:

If the x intercepts are 5 and 6 and the coefficient of is 3:

Create two brackets that satisfy this:

For 3, one bracket must contain 3x and the other x, eg: (3x-n)(x+m)

To let x=5 in the bracket (3x-n), imagine solving it as 3x=n, therefore n=15

To let x=-6 in the bracket (x+m), imagine solving it as x=-m, so m=-6

Therefore, you have (3x-15)(x+6)

To make this a quadratic, expand the terms to get: 3
`x^(2)`-9x-90

Hope this helped :)