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

Answer:

B

Step-by-step explanation:

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

Answer 2

Answer:

1,-1 are rational numbers

Step-by-step explanation:

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

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

⇒ $(x-1)(x+1)(x^2-3)(x^2+2)$

⇒ $(x-1)(x+1)(x+\sqrt{3})(x-\sqrt{3})(x+\sqrt{2})(x-\sqrt{3})$

⇒$(x=1)(x=-1)(x=\sqrt{3})(x=-\sqrt{3})(x=\sqrt{2})(x=-\sqrt{2})$

⇒$x=1,-1,\sqrt{3},-\sqrt{3},\sqrt{2},-\sqrt{2}$

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

Rest $x=\sqrt{3},-\sqrt{3},\sqrt{2},-\sqrt{2}$ are irrational numbers.