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

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

Grade:10

2 Answers

SR Roy
128 Points
5 years ago
Let the roots of given equation be α and β.⇒ Sum of roots = α + β = p ......(1)and product of roots = α β = q .......(2)According to the given condition,Adding (1) and (3), we getOn putting value of α in (3), we getOn putting value of α and β in (2), we getHence Proved
SR Roy
128 Points
5 years ago
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/p²Hence , answer is q/p²

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