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IPMAT Indore 2025 · Question 18 of 90 · Quantitative Ability (MCQ)

IPMAT Indore 2025 — Question 18

If $8 x^{2} - 2 k x + k = 0$ is a quadratic equation in $x$ , such that one of its roots is $p$ times the other, and $p, k$ are positive real numbers, then $k$ equals

A $(p + \frac{1}{p})^{2}$
B $2 (p + \frac{1}{p})$
C $(p + \frac{1}{p})$
D $2 (p + \frac{1}{p})^{2}$

Reveal answer

Correct answer

D.

2 (p + \frac{1}{p})^{2}

Reveal solution

Sum of roots: $α (1 + p) = k /4$ . Product: $p α^{2} = k /8$ . Solving $α = k / (8 p)$ and substituting gives $k = 2 (p + 1/ p)^{2}$ .

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