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Relation between Roots and Coefficients for Quadratic

If α, β are...

Question

If $α, β$ are the roots of $x^{2} + 3 x + 3 = 0$ then find the quadratic equation whose roots are $(α + β)$ and $α β$

x^{2} = 1

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x^{2} = 4

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x^{2} = 9

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None of these

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Solution

The correct option is C $x^{2} = 9$
For the equation, sum of roots $= α + β = - \frac{3}{1} = - 3$
Product of roots $= α \times β = \frac{3}{1} = 3$
So, the eqn with roots $= α + β$ and $α \times β$ is $(x - (- 3)) (x - 3) = 0$
$=> x^{2} - 9 = 0$

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