Question

Α and β are the roots of the quadratic equation x2 + 3x + K = 0 if α2 - β2 = 21, then the value of K is

Answer 1

$\displaystyle p^2-q^2=21\\(p-q)(p+q)=21\\\left(\pm\frac{\sqrt{D}}{a}\right)\left(-\frac{b}{a}\right)=21\\\left(\pm\frac{\sqrt{b^2-4ac}}{a}\right)\left(-\frac{b}{a}\right)=21\\\left(\pm\frac{\sqrt{3^2-4(1)k}}{1}\right)\left(-\frac{3}{1}\right)=21\\\pm\sqrt{9-4k}=-7\\9-4k=49\\-4k=40\\\boxed{\boxed{k=-10}}$