Question

Write the quadratic equation whose roots are -4 and 6 and whose leading coefficient is 3​

Answer 1

3x²-6x-72. The quadratic equation whose roots are -4 and 6 with a leading coefficient of 3 is 3x²-6x-72.

The solutions of a quadratic equation are x = -4 and x = 6 with a leading coefficient of 3. The solutions are two real numbers which means that (x + 4) and (x - 6) are the factors of our unknown quadratic equation and the leading coefficient is 3.

`3(x+4)(x-6)=0`

Expand (x+4)(x-6):

`3(x^(2) -2x-24)=0\\3x^(2) -6x-72=0` which is our quadratic equation.

Answer 2

y = 3x² - 6x - 72

Explanation:

Since the roots are x = - 4 and x = 6 then the factors are

(x + 4) and (x - 6) and the quadratic function is

y = a(x + 4)(x - 6) ← a is a multiplier, in this case 3, so

y = 3(x + 4)(x - 6) ← expand factors and distribute by 3

y = 3(x² - 2x - 24)

y = 3x² - 6x - 72