Q. The quadratic equation whose roots are three times the roots of $3ax^{2} + 3bx + c = 0$ is
A) $ax^{2} + 3bx + 3c = 0$
B) $ax^{2} + 3bx + c = 0$
C) $9ax^{2} + 9bx + c = 0$
D) $ax^{2} + bx + 3c = 0$
Explanation
(a)
Let root of $3ax^{2} + 3bx + c = 0$ be $\alpha$, then
$3a\alpha^{2} + 3b\alpha + c = 0$
According to the given condition,
$\Rightarrow \ \ \ \ x = 3\alpha$
$\Rightarrow \ \ \ \alpha = \frac{x}{3}$
$\therefore\ \ \ 3a\frac{x^{2}}{9} + 3b\frac{x}{3} + c = 0$
$\Rightarrow \ \ \ ax^{2} + 3bx + 3c = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.