Question

If 1 is the one of the zeroes of the polynomial 7x-x^3-6.find its other zeroes.Answer this question faster ​

Answer 1

$\Huge{\blue{\underline{\textsf{Answer}}}}$

$\large{\red{\underline{\tt{Given:}}}}$

1 is the one of the zeroes of the polynomial

$7x - x^{3} - 6$

$\large{\red{\underline{\tt{Solution:}}}}$

When (x-1) is a factor of 7x-x³-6

$\implies\rm -(x^3-7x+6)$

$\implies\rm -(x^3-x^2+x^2-x-6x+6)$

$\implies\rm -[(x^3-x^2)+(x^2-x)-6(x-1)$

$\implies\rm -[x^2(x-1)+x(x-1)-6(x-1)]$

$\implies\rm -(x-1)(x^2+3x-2x-6)$

$\implies\rm -(x-1)[(x^2+3x)-(2x+6)]$

$\implies\rm -(x-1)[x(x+3)-2(x+3)]$

$\implies\rm -(x-1)(x+3)(x-2)$

So Therefore other factor of the polynomial are (x+3) and (x-2).