Question

Find all the zeroes of the polynomial $x^{2} - 8x^{3} + 19x^{2} - 12x + 2$,if two of its zeroes are 2+√2 and 2-√2

Answer 1

Answer:

Let f(x)=x

4

−8x

3

+18x

2

−8x+2

Substituting x=2+

3

, we get

f(2+

3

)=(2+

3

)

4

−8(2+

3

)

3

+18(2+

3

)

2

−8(2+

3

)+2

=(2+

3

)

2

((2+

3

)

2

+18)−8(2+

3

)((2+

3

)

2

+1)+2

=(7+4

3

)(4

3

+25)−8(2+

3

)(8+4

3

)+2

=175+48−128−96+2

=1

Hence, option B is correct.

Answer 2

Find all the zeroes of the polynomial $x^{2} - 8x^{3} + 19x^{2} - 12x + 2$,if two of its zeroes are 2+√2 and 2-√2