Q13 of 113 Page 50

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 = x2–(α + β) x + αβ


= x2–(- 4)x + (-12)


= x2 + 4x – 12


Now, sum of zeroes =


Product of zeroes =


Hence, relationship verified.


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