Question

show that thr polynomial f(x) = x⁴+4x²+6 has no zeros

Answer 1

Above is the answer.
i.e
that is f(x) has no zero.

Hope it helps you.

Answer 2

Answer:

The given polynomial has no zeros.

Step-by-step explanation:

Given : Polynomial  $f(x) = x^4+4x^2+6$

To find : Show that the polynomial has no zeros.

Solution :

First we start making factors,

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

$x^4+4x^2+4+2=0$  

$x^4+4x^2+2^2+2=0$

Apply property, $(a+b)^2=a^2+b^2+2ab$

$(x^2+2)^2+2=0$

Now, $(x^2+2)^2=-2$

There is no real solution.

Therefore, The given polynomial has no roots.