Question

Find the quadratic polynomial whose zeroes are 1 and 3. Verify the relation
between the coefficients and the zeroes of the polynomial.​

Answer 1

Answer:

Let the zeroes of the quadratic polynomial be α=1,β=−3

Then, α+β=1+(−3)=−2

αβ=1×(−3)=−3

Sum of zeroes =α+β=−2

Product of zeroes =αβ=−3

Then, the quadratic polynomial =x^2 −( sum of zeroes )x+ product of zeroes =x^2 −(−2)x+(−3)=x^2 +2x−3

Verification:

Sum of zeroes =α+β=1+(−3)=−2 or

Coefficient of x

2

Coefficient of x

=−

1

(2)

=−2

Product of zeroes =αβ=(1)(−3)=−3 or

=

Coefficient of x

2

Constant term

=

1

−3

=−3

So, the relationship between the zeroes and the coefficients is verified.