What is the relation between zeroes and coefficients of the given quadratic polynomial?

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Solution

Determine the relation between zeroes and coefficients of the given quadratic polynomial.
The standard form of the quadratic polynomal is $f (x) = a x^{2} + b x + c, a \neq 0$ .
Let $α$ and $β$ be the two zeros of the polynomial.
The required relation between zeroes and coefficients of the given quadratic polynomial is:
The sum of zeros, $α + β = \frac{- b}{a}$ .
The product of zeros, $α β = \frac{c}{a}$ .
Hence, the solution is the sum of zeros is $\frac{- b}{a}$ and the product of zeros is $\frac{c}{a}$ .

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