Question

Find all zeros 5x^4+126x^2+25 Need help setting up.

Answer 1

Make the substitution y=x^2 Doing this you get:
\[5x^4+126x^2+25=5y^2+126y+25\]
Now factor this:
\[5y^2+126y+25=(5y+1)(y+25)\]
But remember, y=x^2, so:
\[(5x^2+1)(x^2+25)\]
And this doesn't factor any further on the real numbers.

Answer 2

So there are no x-intercepts. (zeros)

Answer 3

The fact that there are no zeros can be discovered by looking at the equation. Since x^4 has a minimum value of 0 and x^2 has a minimum value of 0, the y value will never be less than 25 so it could never cross the x axis. Thus no zeros.

Answer 4

Thankk youu!

Answer 5

yw