Question

if alpha and beta are the zeros of quadratic polynomial aX square + bx + c then find the value of Alpha square beta + beta square alpha

Answer 1

Hey mate !!

Here's the answer !!

Given : 

Equation = ax² + bx + c   -----( 1 )

To find :

α²β + αβ²

Proof :

Let's simplify the Rule that has to be found. We can take α and β as common outside. After taking common we get,

αβ ( α + β )

We know that,

Product of zeros ( αβ ) = c / a

Sum of zeros ( α + β ) = - b / a

From the equation ( 1 ) given we get,

a = a, b = b, c = c

Substituting them in the formulas we get,

=> αβ ( α + β ) = c / a ( - b / a )

= c * - b / a * a

= - bc / a²

Hence α²β + αβ² = - bc / a²

Hope my answer helped !!

Cheers !!

Answer 2

this is easy to solve know......