Question

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Answer 1

Answer:

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Step-by-step explanation:

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

Using alpha +beta and alpha×beta find the sum and product

To find the quadratic equation do 1/alpha + 1/beta and 1/alpha× 1/beta

cross multiply 1/alpha+ 1/beta to get alpha +beta/alpha beta then give the value which u got at first the take 1/alpha ×1/beta and give the value for 1/alpha beta

Last give this value in the equation

X^2-( alpha +beta/alpha beta)x + 1/ alpha beta