Question

If alpha and beta are the zeroes of the quadratic polynomial f(x) = x^2-px+q then find the value of alpha^2+beta^2​

Answer 1

Answer:

Consider the given polynomial

f(x)=x

2

−px+q

α and βare the zeros of given polynomial

We know that,

Sumofzeros=−

cofficentofx

2

cofficentofx

α+β=

1

−(−p)

α+β=p

Productofzeros=

cofficentofx

2

constant

α×β=

1

q

α×β=q

Then,

Part (1):-

α

2

+β

2

=(α+β)

2

−2αβ

α

2

+β

2

=p

2

−2q

Part (2):-

α

1

+

β

1

=

αβ

α+β

=

q

p