Question

The value of ‘a’ for which one root of the quadratic equation $(a^2 − 5a + 3) x^2 + (3a − 1) x + 2 = 0$ is twice as large as the other, is

• A. $\frac{2}{3}$
• B. $-\frac{2}{3}$
• C. $\frac{1}{3}$
• D. $-\frac{1}{3}$

Answer 1

Answer: (A)

$\beta=2\alpha$
$3\alpha=\frac{3a-1}{a^{2}-5a+3}$
$\frac{\left(3a-1\right)^{2}}{a\left(a^{2}-5a+3\right)^{2}}=\frac{1}{a^{2}+5a+6}$
$\Rightarrow a=\frac{2}{3}.$