Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficient.
$4 u^{2} + 8 u$

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Solution

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

zero of the polynomial is the value of $x$ where $p (x) = 0$

putting $p (x) = 0$

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

$4 u (u + 2) = 0$

$4 u = 0 | u + 2 = 0$

$u = 0 | u = - 2$

$∴ α = 0, β = - 2$ are the zeroes of the polynomial

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4 u^{2} + 8 u

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

(ii) $4 s^{2} - 4 s + 1$

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