Question

if alpha and beta are the zeros of the polynomial x² + 3x - 2 (x + 7) then the value of (alpha + 1) (beta + 1) =​

Answer 1

Given: α,β are zeroes of the polynomial 4x

2

+3x+7

To find the value of

α

1

+

β

1

We know that equation ax

2

+bx+c=0

Then sum of roots =

a

−b

and product of roots=

a

c

From the given quadratic equation,

α+β=−

4

3

and αβ=

4

7

Therefore,

α

1

+

β

1

=

αβ

α+β

=

4

7

−

4

3

=−

7

3

⇒

α

1

+

β

1

=−

7

3