Find the sum and product of the zeroes of the following quadratic polynomials.
$4 \sqrt{3} x^{2} + 5 x - 2 \sqrt{3}$

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Solution

The standard form of any polynomial is $(coefficient of x^{2}) x^{2} + (coefficient of x) x + constant term$ .
Here, coefficient of $x^{2}$ is $4 \sqrt{3}$ , coefficient of $x$ is $5$ , and constant term is $- 2 \sqrt{3}$ .
Step 1: To find the sum of zeroes.
Sum of zeroes = $\frac{- (coefficient of x)}{coefficient of x^{2}} = \frac{- 5}{4 \sqrt{3}}$
Step 2: To find the product of zeroes.
Product of zeroes = $\frac{constant term}{coefficient of x^{2}} = \frac{- 2 \sqrt{3}}{4 \sqrt{3}} = - \frac{1}{2}$
Hence, the sum and product of zeroes are $\frac{- 5}{4 \sqrt{3}}$ and $- \frac{1}{2}$ respectively.

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