Question

obtain all zeroes if f (x)=2x^4-3x^3-3x+6x-2 if two zeroes are root 2 and -root 2​

Answer 1

Step-by-step explanation:

The given polynomial is

f(x)=2x⁴-3x³-3x²+6x-2

The given zeroes are√2 and -√2

So x+√2 and x-√2 are the factors of f(x)

So (x-√2)(x+√2)=x²-2 is a factor of f(x).

Now ,

2x⁴-3x³-3x²+6x-2

=2x⁴-4x²-3x³+6x+x²-2

=2x²(x²-2)-3x(x²-2)+1(x²-2)

=(x²-2)(2x²-3x+1)

Now factorising

2x²-3x+1

=2x²-2x-x+1

=2x(x-1)-1(x-1)

=(x-1)(2x-1)

now (x-1)(2x-1)=0

=> x-1=0 or 2x-1=0

=> x=1 or x=1/2

Thus the other two zeroes are 1 and1/2.

Hope you got it.