Question

If alpha and beta are the zeroes of the polynomial 3x^2-5x-2 evaluate alpha^2+beta^2

Answer 1

Hy!!

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Let ax^2 + bx + c be 3x^2-5x-2..

Here (alpha + beta) = - b/a

= - (-5) / 3

= 5/3

And (alpha * beta) = c/a

= - 2/3

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Since, alpha^2 + beta^2

= (alpha + beta) ^2 - 2(alpha * beta)

Put their values,

= (5/3)^2 - 2(-2/3)

= 25/9 + 4/3

= (25 + 16) / 9

= 41/9

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Hope it's helpful to u.