JEE Main 2022 · 25 Jul · Shift 1 · Mathematics Q24

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MathematicsInteger+4 / -1Question 24 of 90

Let a, b be two non-zero real numbers. If p and r are the roots of the equation $x^2-8ax+2a=0$ and q and s are the roots of the equation $x^2+12bx+6b=0$ , such that $\dfrac1p,\dfrac1q,\dfrac1r,\dfrac1s$ are in A.P., then $a^{-1}-b^{-1}$ is equal to ______.

Your answer

Answer and worked solution

Official answer: 38

Reciprocals. $\frac1p,\frac1r$ are roots of $t^2-4t+\frac1{2a}=0$ ; $\frac1q,\frac1s$ of $t^2+2t+\frac1{6b}=0$ . The AP is $5,2,-1,-4$ .

Products. $\frac1{2a}=-5$ , $\frac1{6b}=-8$ : $a^{-1}=-10$ , $b^{-1}=-48$ , difference 38.

Answer: 38

Topics:Arithmetic progression Roots and coefficients

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JEE Main 2022 · 25 Jul · Shift 1, Mathematics question 24