If alpha and beta are the zeroes of the polynomial 2y 2 + 7y+5 find the value of alpha 2 and beta 2 .
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2y²+7y+5=0
let α and β be 2 roots
sum of roots = α+β = - coeff of y/ coeff of y² = -7/2
product of roots = αβ = constant / coeff of y² = 5/2
(α+β)² = α²+β²+2αβ ⇒ (5/2)² = α²+β²+2(-7/2)
α²+β² = 53/4
that's all
let α and β be 2 roots
sum of roots = α+β = - coeff of y/ coeff of y² = -7/2
product of roots = αβ = constant / coeff of y² = 5/2
(α+β)² = α²+β²+2αβ ⇒ (5/2)² = α²+β²+2(-7/2)
α²+β² = 53/4
that's all
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