Question

Fnd the value of q so that the equation 2x^2-3px+5q=0 has one root which id twice the other

Answer 1

value of q would be p²/5.

let one root of given equation is k then other root is 2k [ according to question, ]

sum of roots = - coefficient of x/coefficient of x²

⇒k + 2k = -(-3)/2 = 3p/2

⇒3k = 3p/2

⇒k = p/2........(1)

now product of roots = constant/coefficient of x²

⇒k(2k) = 5q/2

⇒2k² = 5q/2

from equation (1) we get,

2(p/2)² = 5q/2

⇒2p²/4 = 5q/2

⇒p² = 5q

⇒q = p²/5

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