Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients:

x^{2} + 7x + 12

Let f(x) = x^{2} + 7x + 12

Put f(x) = 0

x^{2} + 7x + 12 = 0

x^{2} + 4x + 3x + 12 = 0

3(x + 4) + x(x + 4) = 0

(3 + x) (x + 4) = 0

∴ x = -4 or x = -3

Now,

sum of zeroes = -3 + (-4) = -7=

Product of zeroes = (-3) × (-4)

Hence, relationship verified.

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