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:
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
2nd 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