Question

It being given that 1 is a zero of the polynomial (7x - x^3- 6), find its other zeroes. ​

Answer 1

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It being given

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.

HOPE U UNDERSTAND.

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