Question

if alpha and beta are the zeroes of the polynomial 2x^2 +3x -6 then find the value of alpha^2 + beta^2

Answer 1

Answer:

2x2+x-6=2x2+4x-3x-6=2x(x+2)-3(x+2)

(2x-3)(x+2)x=3/2 and x - 2let alpha

3/2 and beta -2so 2 alpha and 2 beta

is 2x3/2=3= 2 alpha and 2 beta =

-4so now 2 alpha 2 beta 3+(-4)-1 and

2 alpha x 2 beta 3x(-4) -12so are

quadratic equation will be x- sum of

zeroes)x (product of zeroes)=x2-(-1)x

(-12)=x2+x-12

Answer 2

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 + β²

Now 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

$\Huge{\boxed{\sf{= \dfrac{33}{4}}}}$