Question

If one of the roots of the equation x2 - px + q = 0 is m times the other root, then
m/(1+m2)
is equal to?

Answer 1

I think question is ----->If one of the roots of the equation x2 - px + q = 0 is m times the other root, then m/(1 + m)² equal to ?

Let one root of x² - px + q = 0 is α then, other root must be mα [ A/C to question]
∵ sum of roots = -coefficient of x/coefficient of x²
⇒ α + mα = -(-p)/1 = p
⇒ α(1 + m) = p -------------(1)

∵ product of roots = constant/coefficient of x²
⇒ α.mα = q/1
⇒ mα² = q -------(2)
Put equation (1) in equation (2) ,
m × p²/(1 + m)² = q
⇒ m/(1 + m)² = q/p²

Hence , answer is q/p²

Answer 2

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