Find the zeroes of the polynomial $f (x) = 4 x^{2} + 8 x$ and verify the relationship between the zeroes and its coefficients.

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Solution

Given polynomial can be written as $4 x^{2} + 8 x = 4 x (x + 2) = 0$
Hence the roots are $x = 0, x = - 2$
The sum of roots are $\frac{- b}{a} = - 2$
and the product of roots are $\frac{c}{a} = 0$

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