Question

find the zero's of x2+5x-6 and check the relation between quotient of polynomial and zeroes of polynomial​

Answer 1

$equation \: is \: wrong \: {x}^{2} + 5x - 6 \\ \\ Q.1 \: \: find \: the \: zeores \: of \: {x}^{2} + 5x + 6 \: and \: \\ check \: the \: relation \: between \: coefficients \: of \\ \: polynomial \: and \: zeroes \: of \: polynomial ? \\ \\ ans. \: \: {x }^{2} + 5x + 6 \\ \\ = > {x}^{2} - ( - 3 - 2)x + 6 \\ \\ = > {x}^{2} + 3x + 2x + 6 \\ \\ = > x(x + 3) + 2(x + 3) = 0\\ \\ = > (x + 3)( x + 2) = 0 \\ \\ x = - 3 \: and \: x = - 2 \: are \: zeroes \: of \: this \: equation. \\ \\ \\ verification \\ \\ \\ = > \alpha + \beta = \frac{ - b}{a} \\ \\ = >( - 3) + (- 2) = \frac{ - (5)}{1} \\ \\ = > - 5 = - 5 \\ \\ and \: \\ \\ = > \alpha \times \beta = \frac{c}{a} \\ \\ = > - 3 \times - 2 = \frac{ -6}{1} \\ \\ = > 6 = 6 \: \: hence \: proved.$