The sum of all zeroes of the polynomial p(x) = $5 x^{5} - 20 x^{4} + 5 x^{3} + 50 x^{2} - 20 x - 40$ is _ and the product is _ .

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Solution

For any polynomial,

Sum of zeroes $= \frac{- b}{a} = \frac{20}{5} = 4$

Product of zeroes $= \frac{- z}{a}$ [This is the formula for odd degree polynomials. For even degree polynomials, product of zeroes $= \frac{z}{a}$ , where z is the constant term]
$= \frac{40}{5} = 8$

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The sum of all zeroes of the polynomial p(x) = $5 x^{5} - 20 x^{4} + 5 x^{3} + 50 x^{2} - 20 x - 40$ is

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