Question

Find the quadratic polynomial, sum of whose zeros is 8 and their product is 12. Hence, find the zeros of the polynomial.

Answer 1

Given:

Sum of zeros = 8

Product of zeros = 12

Step-wise calculation:

1. A quadratic polynomial with zeros α and β can be written (monic) as x² – (α + β)x + αβ.

2. Substitute the given sum and product: 

f(x) = x² – 8x + 12

3. Factorize f(x): 

x² – 8x + 12 = (x – 2)(x – 6)

4. Set each factor to zero to find the zeros: 

x – 2 = 0 

⇒ x = 2

x – 6 = 0 

⇒ x = 6

Required quadratic polynomial: x² – 8x + 12.

Zeros of the polynomial: 2 and 6.