Question

The function $g$ is defined by $g\left(x\right)=6x^2+x-2$. In the $x-y$ plane, the graph of $y=g\left(x\right)$ crosses the $x$-axis at $x=a$. Which of the following can be the value of $a$?

• A. $\frac{1}{2}$
• B. $1$
• C. $\frac{3}{2}$
• D. $2$
• E. $\frac{5}{2}$

Answer 1

The correct option is A $\frac{1}{2}$

As given $y=g\left(x\right)$ crosses the $x$-axis at $x=a$,which means that $y=0$ at $x=a$
So, $y=g\left(x\right)=0$ when $x$ $=a$.
We set $g\left(x\right)=0$ and solving for $x$,
$\Rightarrow 6x^2+x-2=0$
$\Rightarrow (2x-1)(3x-2)=0$
So, either $2x-1=0$ ; $x=\frac{1}{2}$
$\Rightarrow 3x-2=0$ ; $x=\frac{2}{3}$
Since, we have only one value provided in the answer i.e $\frac{1}{2}$.
Hence,choice A is correct.