Question

How do you find the real solutions of the polynomial `14x^2+5=3x^4`?

Answer 1

See below

Explanation:

`14x^2 + 5 = 3x^4`
`0 = 3x^4 - 14x^2 - 5`
`0 = 3x^4 - 15x^2 + x^2 - 5`
`0 = 3x^2(x^2-5) + 1(x^2-5)`
`0 = (3x^2+1)(x^2-5)`

`0 = 3x^2 + 1`
`-1 = 3x^2`
`-1/3 = x^2`
`+-sqrt(-1/3) = x`
These roots are not real.

`x^2 - 5 = 0`
`x^2 = 5`
`x = +-sqrt5`
These roots are real.