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

1 Answer
Noah G
Aug 27, 2017

#{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!

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