Answer
See below
Work Step by Step
Given: $y=2x^2-11x+5$
The x-intercept of this function's graph occurs at $x$ such that $y=0$.
Then $2x^2-11x+5=0$
The solution to this equation is: $x=\frac{-(-11)\pm \sqrt (-11)^2-4.2.5}{2(2)}=\frac{11 \pm\sqrt 81}{4}=\frac{11 \pm 9}{4}$
Hence, $x=5 \lor x=0.5$
From the graph, we can see that the solution is $0.5 \lt x \lt 5$
