Multiple choice

$\alpha,\beta$ be the roots of the equation ${ x }^{ 2 }-3x+a=0$ and $\gamma ,\delta $ the roots of ${ x }^{ 2 }-12x+b=0$ and numbers $\alpha ,\beta ,\gamma ,\delta $ (in this order) form an increasing G.P, then

  1. $a=3,b=12$
  2. $a=12,b=3$
  3. $a=2,b=32$
  4. $a=4,b=16$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the four increasing GP terms be t, tr, tr^2, and tr^3. Since the first pair sums to 3 and the second pair sums to 12, r^2 = 4, so r = 2 and the terms are 1, 2, 4, 8, giving a = 2 and b = 32.

Keep practicing — related questions