Question

Find all the zeroes of the polynomial x^4-3x^3 +6x-4, if two of its zeroes are √2 and -√2
Pls answer quick

Answer 1

Here p(x)=x^4-3x^3+0x^2+6x-4
The two zeroes are √2,-√2
x=√2 , x=-√2

So, (x-√2)(x+√2)will be a factor of p(x)

So,(x^2-2) will be a factor of p(x)

a^2-b^2=(a-b)(a+b)

Now dividing p(x)by (x^2-2)

We will get x^2-3x+2 as a quotient

Since x^2-3x+2 is a quotient So, it will also be a factor of p(x)

So,
x^2-3x+2
=x^2-2x-x+2 (mid term factorisation)
=x(x-2)-1(x-2)
=(x-2)(x-1)
The zeroes of p(x) are given when p(x)=0
So,
(x-2)=0 or (x-1)=0
x=2 or x=1

Answer :- The zeroes of p(x) are √2,(-√2),2,2

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