Solve the inequality 2x^2-3x+1=

According to the rule, between the values of the roots of
the equation 2x^2-3x+1=0, the expression has the opposite sign to the sign of the
leading coefficient. Outside the roots, the expresison has the same sign as the sign of
the leading coefficient.

We'll identify the sign of the
leading coefficient a = 2, so the sign is "+".

Therefore,
the expression is negative between the value of the
roots.

We'll detemrine the roots of the equation
2x^2-3x+1=0.

We'll apply the quadratic
formula:

x1 =
[3+sqrt(9-8)]/4

x1 =
(3+1)/4

x1 = 1

x2 =
(3-1)/4

x2 =
1/2

The expression 2x^2-3x+1 is negative,
2x^2-3x+1 =< 0, if x belongs to the interval [1/2 ;
1].