Explain what are x values for the inequality 2x^2-7x+3<0.

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giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

If we'll draw the graph of the function it will be a concave upward parabola. The vertex of parabola is aminimum point.

f(x) = 2x^2-7x+3

The area between the roots of quadratic is the area where parabola goes below the x axis. This area represents the solution of the inequality.

First, we'll determine the roots of the quadratic:

2x^2-7x+3 = 0

We'll apply the quadratic formula:

x1 = [7+sqrt(49 - 24)]/4

x1 = (7+sqrt25)/4

x1 = (7+5)/4

x1 = 3

x2 = (7-5)/4

x2 = 1/2

The expression 2x^2-7x+3 is negative when x belongs to the range  (1/2 ; 3).

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

2x^2-7x+3 < 0.

WE factorise the left to solve the inequality.

2x^2-6x-x+3 < 0

2x(x-3)-1(x-3) < 0

(2x-1)((x-3) < 0.So x= 1/2 and x = 3 are the zeros of the quadratic 2x^2-7x+3 .

So for 1/2 < x < 3, LHS is negative .

 

 

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thecoolsundar | eNotes Newbie

Posted on

first solve;

2x^2-7x+3 = 0

Only one of the solutions is less than 0.

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