Question

Form a quadratic polynomial whose zeroes are 1 and –3. Verify the relation

between the coefficients and 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 =x2−( sum of zeroes )x+ product of zeroes =x2−(−2)x+(−3)=x2+2x−3

Verification:

Sum of zeroes =α+β=1+(−3)=−2 or 

=− Coefficient of x2 Coefficient of x=−1(2)=−2

Product of zeroes =αβ=(1)(−3)=−3 or 

= Coefficient of x2 Constant term =1−3=−3

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