Question

find the zeroes of polynomial x^4-3x^2+2 by using factor theorem
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Answer 1

QUESTION-:

find the zeroes of polynomial x⁴-3x²+2 by using factor theorem

EXPLANATION-:

First let's factorize the given expression using splitting the middle term method

So let's get started!

Here in the given expression we need 2 numbers whose sum us -3 and produce is 2 .

The numbers can be -2,1

Now,

→x⁴-3x²+2

Now,rewrite the expression as-:

→(x²-2)(x²-1)

Now using identity a²-b²=(a+b)(a-b)

→(x²-2)(x²-1²)

→(x²-1)(x+1)(x-1)

So the factors are-:

(x²-1),(x+1),(x-1)

So zeroes will be-:

→x²-1=0

→x²=1

→x=±1

→x=1,-1

So zeroes are 1 and -1