Question

Write the quadratic equation whose roots are −6 and −4 , and whose leading coefficient is 5 .

Answer 1

Vieta's formulas :

s = x₁ + x₂ = -6 + (-4) = -6 - 4 = -10

p = x₁ · x₂ = -6·(-4) = +24 = 24

The equation is :  5(x² - sx + p) = 0 ⇒ 5(x² +10x +24) = 0 ⇒

⇒ 5x² + 50x + 120 = 0.