Question

sum of the zeroes of a second degree polynomial is –2 and their product is 6. The polynomial is​

Answer 1

Given: Sum is -2 and product is 6

To find: The polynomial equation

Solution:

Let the zeros be α = 2 and β = −6.

⇒  Sum of zeros = α + β

                           = 2 + (−6)

                           =−4

⇒  Product of zeros = α × β

                                 = 2 × (−6)

                                 = −12

⇒  Quadratic polynomial = $x^{2} - (\alpha + \beta )x + \alpha \beta$

                                         =  $x^{2} - (-4)x + (-12)$

                                         = $x^{2} +4x-12$