Question

it is given that one is one of the zeros of the polynomial 7 x minus x cube minus 6 find the other 0​

Answer 1

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

Factories the polynomial so that x-1 becomes on of its factor 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-2) (x+3)

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

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

HOPE U UNDERSTAND

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