Find the quadratic polynomial whose zeros are 2 and ‒6. Verify the relation between the coefficients and the zeros of the polynomial.

Question

Philoid · Accepted Answer

Let α = 2 and β = -6

Now, Sum of zeros, α + β = 2 – 6 = -4

And, product of zeroes, αβ = 2(-6) = -12

We know that,

Required polynomial = x²–(α + β) x + αβ

= x²–(- 4)x + (-12)

= x² + 4x – 12

Now, sum of zeroes =

Product of zeroes =

Hence, relationship verified.