Question

If the graph of $y=3x^2+2\sqrt{b}x+5$ does not touch $x$-axis, which of the following is true?

• A. $b>50$
• B. $b>15$
• C. $b<50$
• D. $b<15$

Answer 1

The correct option is D

$b<15$

Given $y=3x^2+2\sqrt{b}x+5$

If $D>0$ $\Rightarrow$ Graph touches $x$-axis at $2$ points.

$D=0$ $\Rightarrow$ Graph touches $x$-axis at $1$ point.

$D<0$ $\Rightarrow$ Graph don't touch $x$-axis.

$\Rightarrow D=b^2-4ac={\left(2\sqrt{b}\right)}^2-4\left(3\right)\left(5\right)<0$

$\Rightarrow 4b<4\left(3\right)\left(5\right)$

$\Rightarrow b<15$