Q4 of 23 Page 1

Attempt any two of the following sub questions:

and , find the quadratic equation whose roots are and .

Given: α + β = 5 …(1) and α3 + β3 = 35 …(2)

We know that (x + y) 3 = x3 + y3 + 3xy(x + y)


⇒ (α + β) 3 = α3 + β3 + 3αβ(α + β)


⇒ 53 = 35 + 3αβ × 5


⇒ 125 - 35 = 15 αβ



Hence, the equation whose roots are α and β will be of the form


x2 – (α + β)x + αβ = 0


⇒ x2 – 5x + 6 = 0


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4

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Attempt any two of the following sub questions:

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