Question

if alpha and beta are the zeroes of quadratic equation then evaluate: Alpha^2/beta+beta^2/alpha​

Answer 1

Answer:

Given quadratic polynomial is f(x)=ax

2

+bx+c

The zeroes of the polynomial are αβ

Sum of the zeros =−

a

b

α+β=>−

a

b

Poduct of the zeros=

a

c

αβ=>

a

c

Now,

α+β=>−

a

b

Squaring both sides,

=>(α+β)

2

=−(

a

b

)

2

=>α

2

+β

2

+2αβ=

a

2

b

2

=>α

2

+β

2

+2(

a

c

)=

a

2

b

2

=>α

2

+β

2

=

a

2

b

2

−

a

2c

=>α

2

+β

2

=

a

2

b

2

−2ca

=>α

2

+β

2

=

a

2

b

2

−2ac