Find the quadratic polynomial, sum of whose zeros is 8 and their product is 12. Hence, find the zeros of the polynomial

Let the zero of the polynomial be α and β

According to the question,

α + β = 8

αβ = 12

∴f(x)= x^{2} – (α + β)x + (αβ)

=x^{2} - 8x + 12

∴required polynomial f(x) = x^{2} - 8x + 12

Put f(x) = 0

x^{2} - 8x + 12 = 0

x^{2} - 6x -2x + 12 = 0

x(x – 6) -2(x – 6) = 0

(x - 6)(x - 2)=0

x = 6 or x = 2

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