It being given that 1 is a zero of the polynomial (7x-x-6), find itsot

1.	It being given that 1 is a zero of the polynomial (7x-x-6), find itsother zeros.XAMPLE 10
Answer» 1 is one of the zeros of the given polynomial 7x - x^3 - 6=0 when x = 1 , 7x - x^3 - 6 = 0 => x - 1 is a factor of the polynomial 7x -x^3 - 6=0 Factorize the polynomial so that x - 1 becomes one of its factors now, 7x - x^3 - 6 = - (x^3 - 7x + 6) = - (x^3 - x^2 + x^2 - x - 6x + 6) = - {(x*3 - x^2) + (x^2 - x) - 6(x - 1)} = - {x^2(x - 1) + x(x - 1) - 6(x - 1)} = - (x - 1)(x^2 + x - 6) - (x -1){ x^2 + 3x - 2x - 6} = - (x - 1){(x^2 + 3x) - (2x + 6)} = - (x - 1){x(x + 3) - 2(x + 3)} = - (x - 1)(x + 3)(x - 2) The other factors of the polynomial are (x + 3) and (x - 2). The other roots of the polynomial is -3 and 2.

It being given that 1 is a zero of the polynomial (7x-x-6), find itsother zeros.XAMPLE 10

Answer»

1 is one of the zeros of the given polynomial 7x - x^3 - 6=0

when x = 1 , 7x - x^3 - 6 = 0 => x - 1 is a factor of the polynomial 7x -x^3 - 6=0

Factorize the polynomial so that x - 1 becomes one of its factors now, 7x - x^3 - 6

= - (x^3 - 7x + 6)

= - (x^3 - x^2 + x^2 - x - 6x + 6)

= - {(x*3 - x^2) + (x^2 - x) - 6(x - 1)}

= - {x^2(x - 1) + x(x - 1) - 6(x - 1)}

= - (x - 1)(x^2 + x - 6)

- (x -1){ x^2 + 3x - 2x - 6}

= - (x - 1){(x^2 + 3x) - (2x + 6)}

= - (x - 1){x(x + 3) - 2(x + 3)}

= - (x - 1)(x + 3)(x - 2)

The other factors of the polynomial are (x + 3) and (x - 2).

The other roots of the polynomial is -3 and 2.