Find the zeros of the following quadratic polynomials and verify the relationship between the zeros and the coefficients.
$4 u^{2} + 8 u$

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Solution

Let $f (u) = 4 u^{2} + 8 u$

To calculate the zeros of the given equation, put $f (u) = 0$ .

$4 u^{2} + 8 u = 0$

$4 u (u + 2) = 0$

$u = 0, u = - 2$

The zeros of the given equation is $0$ and $- 2$ .

Sum of the zeros is $0 + (- 2) = - 2$ .

Product of the zeros is $0 \times - 2 = 0$ .

According to the given equation,

The sum of the zeros is,

$\frac{- b}{a} = \frac{- (8)}{4}$

$= - 2$

The product of the zeros is,

$\frac{c}{a} = \frac{0}{4}$

$= 0$

Hence, it is verified that,

$s u m o f z e r o s = \frac{- c o e f f i c i e n t o f x}{c o e f f i c i e n t o f x^{2}}$

And,

$p r o d u c t o f z e r o s = \frac{c o n s t a n t t e r m}{c o e f f i c i e n t o f x^{2}}$

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Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients.
(i) $x^{2} - 2 x - 8$

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