Question

The zeros of the polynomial $7x^2-\frac{11}{3}x-\frac{2}{3}$ are
(a) $\frac{2}{3},\frac{-1}{7}$
(b) $\frac{2}{7},\frac{-1}{3}$
(c) $\frac{-2}{3},\frac{1}{7}$
(d) none of these

Answer 1

$$\begin{gathered} \left(\text{a}\right)\frac{2}{3},\frac{-1}{7} \\ \text{Let}f\left(x\right)=7x^2-\frac{11}{3}x-\frac{2}{3}=0 \\ \Rightarrow 21x^2-11x-2=0 \\ \Rightarrow 21x^2-14x+3x-2=0 \\ \Rightarrow 7x(3x-2)+1(3x-2)=0 \\ \Rightarrow (3x-2)(7x+1)=0 \\ \Rightarrow x=\frac{2}{3}\text{or}x=\frac{-1}{7} \end{gathered}$$