Question

for what value of m,one zero of the quadratic polynomial x2-6x+m be doouble of the other

Answer 1

$Let \: x ^{2} - 6x + m = (x - a)(x - 2a) \\ x ^{2} - 6x + m =x^{2} - 2ax - ax + 2a^{2} \\ x ^{2} - 6x + m = \: x^{2} - 3ax + 2a^{2} \\ - 6x = - 3ax \\ a = \frac{ - 6x}{ - 3x} \\ a = 2 \\ then \\ m = 2a^{2} \\ m = 2(2)^{2} \\ m = 8$