# Find the quadratic polynomial whose sum of zeroes is 15 and one of the zero is -3.

Solution) Let α = -3 and let β be the other root.

Now, Sum of zeroes , α + β = 15

⇒ β = 15 - (- 3) = 15 + 3 = 18.

Product of zeroes, αβ = (- 3) (18) = - 54

Therefore, the required quadratic polynomial is

p(x) = x

^{2 }- (sum of zeroes) x + (product of zeroes)

p(x) = x

^{2 }- (α+β )x + αβ

p(x) = x

^{2 }- 15x - 54

Regards!

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