Question

If one root of the equation $a{x}^2+x-3=0$ is $-1$, then what is the other root?

• A. $\frac{1}{4}$
• B. $\frac{1}{2}$
• C. $\frac{3}{4}$
• D. $1$

Answer 1

The correct option is C $\frac{3}{4}$

Let $f\left(x\right)=a{x}^2+x-3=0$

One of the root is $-1$.
Therefore, $f(-1)=a-1-3=0$

$\Rightarrow a=4$
Thus the equation is $f\left(x\right)=4x^2+x-3=0$
$\Rightarrow (4x-3)(x+1)=0$

$\Rightarrow x=\frac{3}{4},-1$
Therefore, the other root is $\frac{3}{4}$.