Question

how many real roots does the equation x^4+6x^2+4=0 have?

Answer 1

Answer:

No real roots exists for the equation $x^4+6x^2+4=0$

Step-by-step explanation:

The given Bi-quadratic equation is $x^4+6x^2+4=0$ and we are required to find the number of real roots the equation has.

Let us assume that $x^2=t$ then the equation becomes as follows

$t^2+6t+4=0$

Now the solution of this equation is

$t=\frac{-6\pm \sqrt{36-4(4)}}{2(1)}\\= > t=\frac{-6\pm \sqrt{20}}{2} =-3\pm\sqrt{5}$

Since $t=x^2$ we can write

$x^2=-3\pm \sqrt{5}\\= > x^2=-3-\sqrt{5}\:and\:x^2=-3+\sqrt{5}\\= > x^2 < 0$

Hence the roots are imaginary.

Therefore,

No real roots exists for the equation $x^4+6x^2+4=0$

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