Solve using quadratic formula: -2x² +5x -3 < 0

Answer 1

solution is x can be any real number except 1<x<3/2

x> or = 3/2 or x< or = 1

graph the quadratic, use desmos or TI83. it's a parabola, always below the x axis except between 1 and 3/2

-2x^2 +5x-3 < 0

-(2x^2 -5x+3) <0

2x^2 -5x +3 > 0

factor

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

both factors must be same sign for product >0

2x-3>0, x>3/2, x-1>0, x>0, together means x>3/2

x must be greater than 3/2

x=2 LS=10, x=3 LS=-6, x=4 LS=-15<0

or both factors <0

2x-3<0, x<3/2 and x-1<0, x<1, together means x<1

then the equality possibility

-2x^2 +5x -3 = 0

2x^2-5x+3 = 0

factor

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

set each factor = 0

2x-3 = 0

2x=3

x =3/2

x-1=0

x =1

x = 1 or 1.5

or

use the quadratic formula

x = -5/-4 + or - (1/4)sqr(25-24)

x = 1.25 + or -.25

x = 1.25+.25 or 1.25-.25

x = 1.5 or 1, x= 3/2 or 1

It's a good check on your answer to solve it more than one way