Question

find the quadratic polynomial whose sum and product of zeroes are -1 and -20 respectively. also,find the zeroes of the polynomial so obtained.​

Answer 1

$sum \: of \: zeroes \: = \alpha + \beta = - 1 \\ product \: of \: zeroes \: = \alpha \times \beta = - 20 \\ {x}^{2} - x( \alpha + \beta ) + \alpha \times \beta \\ {x}^{2} - ( - 1)x + ( - 20) \\ p(x) = {x}^{2} + x - 20$

${x}^{2} + 5x - 4x - 20 \\ x(x + 5) - 4(x + 5) \\ (x + 5)(x - 4)$

zeros of the p(x) are = -5 and 4