Question

if alpha and beta are zeroes of x2-3x+6 find alpha3 +beta3​​

Answer 1

Solution :-

Given Polynomial :-

2x² + 3x - 6

Roots = α and β

So as in a quadratic Polynomial :-

-b/a = Sum of roots = α + β

c/a = Product of roots = αβ

Now in our polynomial

a = 2

b = 3

c = -6

So

Sum of roots = -3/2

Product of roots = -6/2 = -3

Now we have to find out the value of

α² + β²Now as we know

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

So α² + β²

=3/4