Question

One of the roots of the quadratic equation $x^2-12x+c=0$, is thrice the other. Find the value of $a$?

• A. $29$
• B. $28$
• C. $-27$
• D. None of these

Answer 1

The correct option is D None of these

Solution:

Let $\alpha$ be the one root of the equation.

So, other root$=3\alpha$

To find:

Value of $c=?$

Solution:

Sum of roots $=\frac{-b}{a}$, where, $b=-12,a=1$

$\Rightarrow \alpha +3\alpha =12$

$\Rightarrow 4\alpha =12$

$\Rightarrow \alpha =3$

Product of roots $=\frac{c}{a}$

$\Rightarrow \alpha \times 3\alpha =c$

$\Rightarrow 3\times 3^2=c$

$\Rightarrow c=27$

Hence, D is the correct option.