Question

Find all the zeroes of 2x4 – 9x3 + 5x2 + 3x -1, if two of its zeroes are 2 + √3 and 2 - √3

Answer 1

we have,

the given zeroes= 2+√3 and 2-√3.

then the factors are = x-2-√3 and

x-2+√3.

here is your answer:-

the other two zeroes are 1 and -1/2

Answer 2

Answer:

Given =>

P(x) = 2x4 – 9x3 + 5x2 + 3x -1

And the zeros are 2 + √3 and 2 - √3.

Now by using the factor theorem, we have the factors of p(x) as =>

(X-2-√3) and (x-2+√3)

Now, on multiplying the factor we get

=>(x-2-√3) (x-2+√3)

=>X^2 -4x +1

(by using a^2 -b^2 = {a+b}{a-b})

Now dividing p(x) by X^2 -4x +1 we get=> 2x^2 -x-1 as quotient.

Plz, refer to the attachment for the division process.

Now, on using the middle term split method in 2x^2 -x -1 we get=>

2x^2 -x -1

=> 2x^2 -2x+x -1

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

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

So, either x = 1

or x = $\dfrac{-1}{2}$ are the other two zeros of p(x).