Question

How do you solve the polynomial inequality and state the answer in interval notation given `2x^4>5x^2+3`?

Answer 1

`{x| x < -sqrt(3) uu sqrt(3) < x, x in RR}`

Explanation:

Rewrite and solve as an equation:

`2x^4 - 5x^2 - 3 = 0`

We let `u = x^2`, then we cna say

`2u^2 - 5u - 3 = 0`

`2u^2 - 6u + u - 3 = 0`

`2u(u - 3) + 1(u - 3) = 0`

`(2u + 1)(u - 3) = 0`

`u = -1/2 and 3`

`x^2 = -1/2 and x^2 = 3`

The only real solution to this equation is `x = +- sqrt(3)`. If we select test points, we realize that the solutions are `x < -sqrt(3)` and `x> sqrt(3)`.

Hopefully this helps!