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Find a quadratic polynomial whose zeroes are $(5-2\sqrt{3})$ and $(5+2\sqrt{3})$.
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Let $\alpha$ and $\beta$ be the zeroes of the required polynomial.
$\alpha = 5 - 2\sqrt{3}, \beta = 5 + 2\sqrt{3}$
$\alpha + \beta = 10$ (I) (1/2 Mark)
$\alpha\beta = 13$ (II) (1/2 Mark)
$\therefore$ The quadratic polynomial is $x^2 - 10x + 13$ (III) (1 Mark)
$\alpha = 5 - 2\sqrt{3}, \beta = 5 + 2\sqrt{3}$
$\alpha + \beta = 10$ (I) (1/2 Mark)
$\alpha\beta = 13$ (II) (1/2 Mark)
$\therefore$ The quadratic polynomial is $x^2 - 10x + 13$ (III) (1 Mark)