Find the minimum value of x which the expression x3 - 7x2 + 11x - 5 ≥ 0.

Answer: Option C

$$\begin{array}{rl}& x^3-7x^2+11x-5⩾0\\ & \Rightarrow x^3-5x^2-2x^2+10x+x-5⩾0\\ & \Rightarrow x^2\left(x-5\right)-2x\left(x-5\right)+1\left(x-5\right)⩾0\\ & \Rightarrow \left(x-5\right)\left(x^2-2x+1\right)⩾0\\ & \Rightarrow \left(x-5\right){\left(x-1\right)}^2⩾0\\ & \Rightarrow \left(x-5\right)\left(x-1\right)\left(x-1\right)⩾0\\ & \text{So, }x=1\&5\end{array}$$
Equation satisfies at both the values, but the minimum value of these two
x = 1