Question

For which value of x does the graph of y = 2x2 - 7x + 6 cross the x-axis?

Answer 1

you are asking for the x intercept so replace y with 0 and solve

Answer 2

\[y=2x ^{2}-7x+6\]
To find the x-intercept, take y=0
\[0=2x ^{2}-7x+6\]
\[0=2x ^{?}-4x-3x+6\]
\[0=2x(x-2)-3(x-2)\]
\[0=(2x-3)(x-2)\]
\[2x-3=0 ; 2x=3; x=3/2\]
\[x-2=0; x=2\]