Question

If alpha and beta are the zeros of the polynomial 2x²+3x-6then find value of alpha square beta + beta square alpha

Answer 1

Given Polynomial :- 2x² + 3x - 6

a = 2

b = 3

c = -6

Given Roots = α and β

In a quadratic Polynomial :-

-b/a = Sum of roots = α + β

c/a = Product of roots = αβ

So, Sum of roots = -b/a = -3/2

Product of roots = c/a = -6/2 = -3

Now we have to find out the value of α² + β²

Now as we know that a² + b² = (a + b)² - 2ab .

So, α² + β² = (α + β)² - 2 (αβ)

= (-3/2)² - 2(-3)

= 9/4 + 6

= (9 + 24)/4

= 33/4