Condition for roots of a biquadratic eqn. to be real

Question

If b$^2$ >= $4ac$ for the eqn.

ax$^4$ + bx$^2 $ + c=0

Then prove that all the roots of the above eqn. will be real if

1. b<0, a>0, c>0
2. b>0, a>0, c>0

My attempt... I substituted y=x$^2$ and then arrived at the condition D >=0 for real roots which gives me b$^2$ >= 4ac...but this condition is already mentioned in the question so how can i decide based on the signs of a b and c whether the roots are real or not?? Also is assuming y=x$^2$ correct to check if all roots of the given biquadratic are real?

Answer 1

So you know $y=x^2$ is real if $b^2\ge4ac$. In fact, $y=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$. If $y=x^2$, what conditions are necessary for $x$ to be real?