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

$\frac{3}{4}$

Explanation for the correct option:

Find the other root:

Let the other root of the equation is $\alpha$.

Since, $-1$ is a root of the given equation, it satisfies the given equation $a{x}^2+x-3=0$,

$$\begin{gathered} \Rightarrow a{\left(-1\right)}^2+\left(-1\right)-3=0 \\ \Rightarrow a-4=0 \\ \Rightarrow a=4 \end{gathered}$$

Substitute the value of $a$ in the given equation.

$\Rightarrow 4x^2+x-3=0$

Now, the product of roots$=\frac{\mathrm{constant}\mathrm{term}}{\mathrm{coefficient}\mathrm{of}{x}^2}$

$$\begin{gathered} \Rightarrow \alpha \times \left(-1\right)=\frac{-3}{4} \\ \Rightarrow \alpha =\frac{3}{4} \end{gathered}$$

Hence, the correct option is C.