Question

How many zeroes does the polynomial f(x)
= (x-1)(x+1) (x-2) have in all ?
please tell the answer with explanation​

Answer 1

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

As we can see after multiplying all the terms we get highest power as 3.

And hence it have 3 zeroes.

The zeroes are:

$(x-1)=0\\x=1\\(x+1)=0\\x=-1\\(x-2)=0\\x=2$

Also, if a polynomial have 2 as highest power it will have 2 zeroes.

And if it have x⁴ with highest power 4 it will have 4 zeroes.

If any polynomial have only x then its power is 1 and only one zero will be obtained.

Hope it was helpful..