Question

find quadretic polynomial the sum and product of the zeroes are -1/2and-3

Answer 1

The equation is "x^2+1/2x-3"

Answer 2

Given,,
$sum \: of \: zeroes \: \alpha + \beta = \frac{ - 1}{2} \\ product \: of \: zeroes \: \alpha \beta = - 3 \\ p(x) = {x}^{2} - ( \alpha + \beta )x + \alpha \beta \\ = {x}^{2} -( \frac{ - 1}{2} )x + ( - 3) \\ = {x}^{2} + \frac{x}{2} - 3 \\ = \frac{2{x}^{2} + x - 6}{2} \\ = 2 {x}^{2} + x - 6$
Hence,, 2x²+x-6 = 0 is the required polynomial.