Question

On of the zeros of the polynomial f(x) = 2x² + 7x – 4 is
(a) 2
(b) $\frac{1}{2}$
(c) $-\frac{1}{2}$
(d) –2

Answer 1

Given: f(x) = 2x² + 7x – 4

Zero of a polynomial is the value of x at which the polynomial becomes zero.

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

Therefore, zeroes of the polynomial f(x) = 2x² + 7x – 4 are $\frac{1}{2}\mathrm{and}-4.$
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Hence, the correct option is (b).