Question

If a and b are the roots of the equation x² – px + r = 0 and a/2 and 2b be the roots of the equation x² – qx + r = 0. Then the value of r is:

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

1st method: -

Sum of the roots (a + b) = p and Product of the roots (ab) = r

for other equation, a/2 + 2b = q and (ab) = r

From above equations,

a = 2/3 (2p - q) and b = (2q - p)/3

The value of r is

2^nd method: - x² – 3x + 2 = 0 and α = 2 and β = 1 and α/2 = 1 and 2β = 2 forms the same expression. P = q = 3 and r = 2. Only d) gives r = 2