Question

Find the quadratic polynomial ,the sum of whose zeroes is 5/2 and their product is 1. Hence, find the zeroes of the polynomial.​

Answer 1

Answer:

Given :-

α+β=

2

5

αβ=1

P(x)=x

2

−(α+β)x+αβ

P(x)=x

2

−

2

5

x+1

=2x

2

−5x+2

P(x)=0

2x

2

−5x+2=0

2x

2

−4x−x+2=0

2x(x−2)−1(x−2)=0

(2x−1)(x−2)=0

2x−1=0 & x−2=0

x=

2

1

& x=2 are zeros of P(x)