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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A

Let the roots are $α$ and $2 α$

$\Rightarrow α + 2 α = \frac{1 - 3 a}{a^{2} - 5 a + 3} a n d α .2 α = \frac{2}{a^{2} - 5 a + 3} \Rightarrow 2 [\frac{1}{9} \frac{(1 - 3 a)^{2}}{(a^{2} - 5 a + 3)^{2}}] = \frac{2}{a^{2} - 5 a + 3}$

$\Rightarrow \frac{(1 - 3 a)^{2}}{(a^{2} - 5 a + 3)^{2}} = 9 \Rightarrow 9 a^{2} - 6 a + 1 = 9 a^{2} - 45 a + 27 \Rightarrow 39 a = 26 \Rightarrow a = \frac{2}{3}$

Suggest Corrections

Similar questions

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

3 a

(a^{2} - 5 a + 3) x^{2} - 3 (a - 1) x + 2 = 0

a

(a^{2} - 5 a + 3) x^{2} + (3 a - 1) x + 2 = 0

(a^{2} - 5 a + 3) x^{2} + (3 a - 1) x + 2 = 0

(a^{2} - 5 a + 3) x^{2} + (3 a - 1) x + 2

Join BYJU'S Learning Program