Question

The value of a for which one root of the quadratic equation (a² − 5a + 3)x² + (3a − 1)x + 2 = 0 is twice as large as the other is
1. 2/3
2. 3/2
3. 5
4. 2

Answer 1

Correct Answer - Option 1 : 2/3

Calculation:

Let α, 2α are roots of the equation.

∴ Sum of the equation

⇒ α + 2α = 3α = (1 – 3a)/(a² − 5a + 3)      ----(i)

∴ Product of the roots

⇒ α × 2α = 2α² = 2/(a² − 5a + 3)      ----(ii)

By (i) and (ii) we have,

9α²/2α² = (1 – 3a)/(a² − 5a + 3) × (a² − 5a + 3)/2

⇒ 9 (a² − 5a + 3) = (1 – 3a)²

⇒ a = 2/3

∴ The value of a is 2/3.