Question

if alpha and beta are the zeros of polynomial 2x^2 - 11 x + 12, Then find the value of of Alpha ^2 beta +alpha beta ^2
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Answer 1

Given :

α & β are zeroes of the polynomial 2x² - 11x + 12  

To Find :

Value of α²β + αβ²

Solution :

Compare given equation 2x² - 11x + 12 with ax² + bx + c , we get ,

⇒ a = 2 , b = -11 , c = 12

Then ,

Sum of zeroes , α + β = -b/a = 11/2 ... (1)

Product of zeroes , αβ = c/a = 12/2 = 6 ... (2)

Now , our required value,

⇒ α²β + αβ²

⇒ αβ ( α + β ) ... [ From (1) & (2) ]

⇒ 6 ( 11 / 2 )

⇒ 33