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

Question

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

1 Answer

Impact of this question

1554 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-19T12:59:42

See below

Explanation:

$14 x^{2} + 5 = 3 x^{4}$ $14x^2 + 5 = 3x^4$
$0 = 3 x^{4} - 14 x^{2} - 5$ $0 = 3x^4 - 14x^2 - 5$
$0 = 3 x^{4} - 15 x^{2} + x^{2} - 5$ $0 = 3x^4 - 15x^2 + x^2 - 5$
$0 = 3 x^{2} (x^{2} - 5) + 1 (x^{2} - 5)$ $0 = 3x^2(x^2-5) + 1(x^2-5)$
$0 = (3 x^{2} + 1) (x^{2} - 5)$ $0 = (3x^2+1)(x^2-5)$

$0 = 3 x^{2} + 1$ $0 = 3x^2 + 1$
$- 1 = 3 x^{2}$ $-1 = 3x^2$
$- \frac{1}{3} = x^{2}$ $-1/3 = x^2$
$\pm \sqrt{- \frac{1}{3}} = x$ $+-sqrt(-1/3) = x$
These roots are not real.

$x^{2} - 5 = 0$ $x^2 - 5 = 0$
$x^{2} = 5$ $x^2 = 5$
$x = \pm \sqrt{5}$ $x = +-sqrt5$
These roots are real.

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you find the real solutions of the polynomial 14x2+5=3x414x^2+5=3x^4?

1 Answer

Explanation:

Related questions

Impact of this question

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