Question

The graph of f(x) = x6 – 2x4 – 5x2 + 6 is shown below. How many roots of f(x) are rational numbers? 1

Answer 1

B

Explanation:

the roots would be 1 and -1 when it comes to the graph

Answer 2

1,-1 are rational numbers

Explanation:

Given equation:
`f(x) = x^6-2x^4-5x^2+6`

Roots of f(x) are :
`x^6-2x^4-5x^2+6=0`

⇒
`(x-1)(x+1)(x^2-3)(x^2+2)`

⇒
`(x-1)(x+1)(x+√(3))(x-√(3))(x+√(2))(x-√(3))`

⇒
`(x=1)(x=-1)(x=√(3))(x=-√(3))(x=√(2))(x=-√(2))`

⇒
`x=1,-1,√(3),-√(3),√(2),-√(2)`

from these roots only -1,1 is consider as rational numbers as all integers are rational numbers.

Rest
`x=√(3),-√(3),√(2),-√(2)` are irrational numbers.