If α, β are the roots of 6x²+ 13x + 7 = 0, then the equation whose roots are α², β² is:

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 4)

Answer 1

Given:

6x2 + 13x + 7 = 0

Concept used:

We know that a quadratic equation whose roots are α and β is given by x² - (α + β) x + αβ = 0

Calculation:

6x2 + 13x + 7 = 0

⇒ x2 + 13x/6 + 7/6 = 0

So, (α + β) = - (13/6)

αβ = 7/6

Now,

(α + β)² = α² + β² + 2αβ

⇒ 169/36 = α2 + β2 + 7/3

⇒ 169/36 - 7/3 = α2 + β2

⇒ (169 - 84)/36 = α2 + β2

⇒ 85/36 = α2 + β2

Now,

x² - (α2 + β2)x + α²β² = 0

⇒ x2 - 85/36x + 49/36 = 0

⇒ 36x2 - 85x + 49 = 0

∴ The required answer is 36x2 - 85x + 49 = 0.

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