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

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 = x^{2}–(α + β) x + αβ

= x^{2}–(- 4)x + (-12)

= x^{2} + 4x – 12

Now, sum of zeroes =

Product of zeroes =

Hence, relationship verified.

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