$If a polynomial (x^{2} + a x - c) cuts x-axis at 2 and -4, the value of a + c is$
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Solution

Suppose $f (x)$ is the polynomial.
Now since it cuts x-axis at 2 and -4, the roots of $f (x)$ are 2 and -4.
Sum of roots = $- a = 2 - 4 = - 2$
$\Rightarrow a = 2$
Product of roots = $- c = 2 \times - 4 = - 8$
$\Rightarrow c = 8$

Hence, $(a + c) = 10$

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