Question

if -1 and 2 are the two zeros of the polynomial 2 x cube minus x square - 5 x minus 2 find its third zero

Answer 1

$here \: \alpha = - 1 \: and \beta = 2 \: we \: need \: to \: find \gamma \\ we \: know \: that \: \alpha + \beta + \gamma = - b \div a \\ so \alpha + \beta + \gamma = 1 \div 2 \\ - 1 + 2 + \gamma = 1 \div 2 \\ so \gamma = - 1 \div 2$

hope it helps thanks

Answer 2

$x ^{3} - ( \alpha + \beta + \gamma ) x {}^{2} + ( \alpha \beta + \beta \gamma + \alpha \gamma )x - \alpha \beta \gamma \\ \alpha \beta \gamma = - x {}^{3} + ( - 1)x {}^{2} - (2)x \\ - x {}^{3} - x {}^{2} - 2x = 0 \\ x {}^{3} + x {}^{2} + 2x = 0 \\ x(x {}^{2} + x + 2) = 0 \\ x {}^{2} + x + 2 = 0 \\ x \: ka \: value \: nikalne \: par \: third \: zero \: ka \: value \: nikal \: jayega.ok$