Question

One of the zeroes of the polynomial$2x^2+7x-4$ is

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

Answer 1

The correct option is B

$\frac{1}{2}$

Zeros of a polynomial can be defined as the points where the polynomial becomes zero as a whole. A polynomial having a value of zero$\left(0\right)$is called zero polynomial.

Zero of the polynomial ⇒$\text{p}\left(x\right)=0$

$$\begin{gathered} 2x^2+7x-4=0 \\ 2x^2-x+8x-4=0 \\ x\left(2x-1\right)+4\left(2x-1\right)=0 \\ \left(2x-1\right)\left(x+4\right)=4 \end{gathered}$$

Let us consider,

$$\begin{gathered} \text{x+4 = 0} \\ \text{x = -4} \end{gathered}$$

which is not among given options

Now consider,

$$\begin{gathered} 2x-1=0 \\ 2x=1 \\ x=\frac{1}{2} \end{gathered}$$

Hence, the correct option is $\frac{1}{2}.$