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

Aug 27, 2017

$\left\{x | x < - \sqrt{3} \cup \sqrt{3} < x , x \in \mathbb{R}\right\}$

#### Explanation:

Rewrite and solve as an equation:

$2 {x}^{4} - 5 {x}^{2} - 3 = 0$

We let $u = {x}^{2}$, then we cna say

$2 {u}^{2} - 5 u - 3 = 0$

$2 {u}^{2} - 6 u + u - 3 = 0$

$2 u \left(u - 3\right) + 1 \left(u - 3\right) = 0$

$\left(2 u + 1\right) \left(u - 3\right) = 0$

$u = - \frac{1}{2} \mathmr{and} 3$

${x}^{2} = - \frac{1}{2} \mathmr{and} {x}^{2} = 3$

The only real solution to this equation is $x = \pm \sqrt{3}$. If we select test points, we realize that the solutions are $x < - \sqrt{3}$ and $x > \sqrt{3}$.

Hopefully this helps!