Question

If alpha and beta are the zeroes of a quadratic polynomial then form a polynomial whose zeroes are 2alpha and 2beta.

Answer 1

Solution :

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Given :

α & β are the zeroes of a polynomial,.

To form a polynomial with zeroes as 2α & 2β

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We know that,

A quadratic equation (or polynomial) is of the form,.

⇒ ax² + bx + c = 0

(or)



⇒ k [x² + (α + β)x + αβ] = 0

then,

⇒ x² + (α + β)x + αβ = 0,.

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if 2α & 2β are the zeroes of the polynomial,.

then, if becomes,.

⇒ x² + (2α + 2β)x + (2α)(2β)

⇒ x² + 2x(α + β) + 4αβ

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                                                   Hope it Helps !!

Answer 2

The answer for this question is x square+2x(a+b)+4ab. Please mark the answer as brilliant.