Question

If 1 is one of the zeroes of the polynomial 7x – x^3 – 6 find all the other zeroes Please help me, I need to submit my assignment in 3 hours! Thank you

Answer 1

I hope it helps.............

Step-by-step explanation:

ATQ

x = 1

thus x - 1 = 0

now when we will divide $- x^{2} + 7x - 6$ by x -1

you will get -x + 6

since -x+6 is the quotient of the polynomial thus it will be equal to 0

therefore

- x + 6 = 0

-x = -6

x = 6

thus the other zero of the polynomial $- x^{2} + 7x - 6$ is 6

Answer 2

Answer:

p(x) =   7x – x^3 – 6

     =  – x^3 +  7x -6

1 is one of the zeroes of p(x)

⇒ x-1 is a factor of p(x)

Dividing p(x) by x-1

(refer to the attachment below)

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

     = -x^2-x+6

    = -1 (x^2+x-6)

   = x^2+x-6

   =  x^2 -2x +3x - 6

   = x(x-2) + 3(x-2)

  = (x+3) (x-2)

x+3=0                  x-2=0

x = -3                   x=2

Hence its other two zeroes are -3 and 2