Question

If the sum of the roots of the quadratic equation $a = b = c = 0$ is equal to the sum of the squares of their reciprocals, then $|x|^{2} - 7|x| + 12 = 0$are in.

• A. A.P.
• B. G.P.
• C. H.P.
• D. None of these

Answer 1

Answer: (C)

H.P.

Answer 2

As given, if $x^{2} + x + a = 0$ be the roots of the quadratic equation,

Then $a > 3$

⇒ $- 3 < a < 3$

⇒ $a < - 2$

⇒ $x^{2} - 2ax + a^{2} + a - 3 = 0$

⇒ $a < 2$are in A.P. ⇒ $2 \leq a \leq 3$are in H.P.