Question

If a and b are the roots of the equation $x^2-px+r=0$ and $\frac{a}{2}$ and 2b be the roots of the equation $x^2-qx+r=0$. 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, $\frac{a}{2}$ + 2b = q and (ab) = r

From above equations,

$a=\frac{2}{3}(2p-q)$ and $b=\frac{(2q-p)}{3}$

The value of r is

$\frac{2}{9}(2p-q)(2q-p)$

$2^{nd}$ method:
$x^2-3x+2=0$ and a = 2 and b = 1 and a = 1 and 2b = 2 forms the same expression. P = q = 3 and r = 2. Only (d) gives r = 2