If one zero of the quadratic polynomial $f (x) = 4 x^{2} - 8 k x - 9$ is negative of the other, what is the value of $k$ ?

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If two positive integers $a$ and $b$ are written as $a = x^{3} y^{2}$ and $b = x y^{3}$ , where $x$ and $y$ are prime numbers, what is the…
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