Question

if one zero of ax^2 + bx + c is double the other zero prove that 2b^2 = 9ac ​

Answer 1

hey mate

your answer:-

We have the following quadratic equation-

ax²+bx+c such that α, 2α are the roots

so, sum of the roots = -b/a = 3α

⇒ α = -b/3a  .......(1)

Products of the roots = c/a = 2α²

Put the value of α from equation (1)

⇒ c/a = 2(-b/3a)²

⇒ c/a = 2b²/9a²

⇒ 2b² = 9ac