$$p^2\geq 4q$$ is the __FILLWRAPl__ condition for the biquadratic equation $$x^4+px^2+q=0$$ to have real roots.

Question

$$p^2\geq 4q$$ is the  __FILLWRAPl__ condition for the biquadratic equation $$x^4+px^2+q=0$$ to have real roots.

Uniteasy Admin · Accepted Answer

If $$p^2\geq 4q$$, the quadratic equation in terms of $$x^2$$ has real roots. If the root for $$x^2$$ is positive, then $$x$$ is also real number after taking square root. If the root for $$x^2$$ is negative, $$x$$ will be complex number. 
Therefore, $$p^2\geq 4q$$ is the  necessary but not sufficient condition for the biquadratic equation $$x^4+px^2+q=0$$ to have real roots.

Multiple Choice Question (MCQ)

Answer