Question

If the graph of $f\left(x\right)=3x^2+6ax+6c$ touches the $x$-axis, then which of the following is always correct?

• A. $a^2=8c$
• B. $c=4a^2$
• C. $a^2=2c$
• D. $c^2=8a$

Answer 1

The correct option is C $a^2=2c$

Given that the graph of $f\left(x\right)=3x^2+6ax+6c$ touches the $x$ axis.
$\therefore$ Discriminant, $D=0$
$\Rightarrow (6a{)}^2–4\times 3\times 6c=0$
$\Rightarrow 36a^2=12\times 6c$
$\Rightarrow a^2=2c$
Hence, the correct answer is option (3).