Write down the quadratic polynomial whose sum and product of zeroes are -1/2 and -3 respectively.

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Solution

$x^{2} - (s u m - o f - z e r o s) x + (p r o d u c t - o f - z e r o s)$

Given, sum of zeros $= - \frac{1}{2}$

product of zeros $= - 3$

$x^{2} - (- \frac{1}{2}) x + (- 3)$

$x^{2} + \frac{1}{2} x - 3$

$2 x^{2} + x - 6 = 0$

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The sum of the zeros and the product of zeros of a quadratic polynomial are $\frac{- 1}{2} a n d - 3$ respectively. Write the polynomial.

\frac{- 3}{2 \sqrt{5}}, - \frac{1}{2}

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