Question

Statement–1 : If the roots of x5 – 40x4 + Px3 + Qx2 + Rx + = 0 are in G.P. and sum of their reciprocal is 10, then || = 32.

Statement–2 : x1. x2. x3.x4.x5 = *, where x1, x2, x3, x4, x5 are the roots of given equation.

(A) Statement –1 is True, Statement – 2 is True; Statement – 2 is a correct explanation for Statement – 1.

(B) Statement – 1 is True, Statement – 2 is True; Statement – 2 is NOT a correct explanation for Statement – 1.

(C) Statement –1 is True, Statement – 2 is False.

(D) Statement – 1 is False, Statement – 2 is True

Answer 1

Correct option (C) Statement –1 is True, Statement – 2 is False.

Explanation:

Roots of the equation x5 – 40x4 + px3 + qx2 + rx + * = 0 are in G.P., let roots be a, ar, ar2 , ar3 , ar4

∴ a + ar + ar2 + ar3 + ar4 = 40 . . . (i)

from (i) and (ii); ar2 = ± 2 . . . (iii)

Now, - * = product of roots = a5 r10 = (ar2)5 = ± 32.

∴ |*| 32 = .

∴ Hence (c) is the correct answer.