CDS 2018 PYQ with Answer — If α and β are two real numbers such that α + β = -q/p and αβ = r/p,…

2018 · Q9

If α and β are two real numbers such that α + β = -q/p and αβ = r/p, where p, q and r are positive real numbers such that p < q < r, then which one of the following is the largest?

Elementary MathematicsAlgebra

A1/(α + β)
B1/α + 1/β
C-1/(αβ)
Dαβ/(α + β)

Explanation

Here alpha + beta = -q/p < 0 and alpha*beta = r/p > 0, so alpha and beta are both negative. The four values are: 1/(alpha+beta) = -p/q, 1/alpha + 1/beta = -q/r, -1/(alpha*beta) = -p/r, alpha*beta/(alpha+beta) = -r/q. With 0 < p < q < r, the smallest magnitude among these is p/r, so -p/r (closest to zero) is the largest. Hence option C.