Question

If $3x^{2} - 5x - 100 = 0$, then x =

• A. 6
• B. –1
• C. 6 or –1
• D. None of these

Answer 1

Answer: (C)

6 or –1

Answer 2

Here $\left\{ \frac{q}{p},pq \right\}$ and 3 are the critical points.

When $\left\{ \frac{p + q}{p},\frac{p + q}{q} \right\}$

$\left\{ \frac{p - q}{p},\frac{p - q}{q} \right\}$The given equation reduces to $a(x^{2} + 1) - (a^{2} + 1)x = 0$

⇒ $a,\frac{1}{a}$

∴ $a,\frac{1}{2a}$ is a solution.

When $x^{4} - 8x^{2} - 9 = 0$

∴ The equation reduces to $\pm 3,\mspace{6mu} \pm 1$⇒ 1=7

∴No solution in this case.

When $\pm 3,\mspace{6mu} \pm i$, the equation reduces to

$\pm 2,\mspace{6mu} \pm i$ ⇒ $ix^{2} - 4x - 4i = 0$

Hence we get, $- 2i$or –1

Trick : By inspection, we have that both the values $2i$ satisfy the given equation.