Given:
[tex]y=3x^2+2px+4q[/tex]
Which has no real roots.
To prove:
[tex]p^2<12q[/tex]
Explanation:
Since it has no real roots.
So, the discriminant becomes,
[tex]\begin{gathered} D<0 \\ \Rightarrow b^2-4ac<0 \end{gathered}[/tex]
Substituting the below values in the inequation.
[tex]\begin{gathered} a=3 \\ b=2p \\ c=4q \end{gathered}[/tex]
We get,
