Question

Write the polynomial of 'x' whose zeroes are 1,-1,2

Answer 1

Answer:

x=1,-1,2

(x-1)(x+1)(x-2)

x²-1(x-2)

x³-2x²-x+2

Answer 2

The polynomial is $x^{3}\ - 2x^{2}\ -\ x\ +\ 2$.

Step-by-step explanation:

As given in question that the polynomial of 'x' whose zeroes are 1, - 1 and 2.

Then, it has the following factor:

(x - 1), (x - (-1)) and (x - 2)

(x - 1), (x + 1) and (x - 2)

So,

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

     = $(x^{2}\ -\ 1^{2})(x\ -\ 2)$

     = $x^{2}(x\ -\ 2) - 1(x\ -\ 2)$

     = $x^{3}\ - 2x^{2}\ -\ x\ +\ 2$

Thus, the polynomial is $x^{3}\ - 2x^{2}\ -\ x\ +\ 2$.