Verified answer

Answer:

1. the roots are x = 1/2 and -2

2. the roots are x = 4 and -2/3

3. the roots are x = -1/4 and -3

Step-by-step explanation:

1. 2x^2 + 3x - 2 = 0 factor it

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

2x - 1 = 0 transpose -1 to other side

2x =1 divide both side by 2

x = 1/2

x + 2 = 0 transpose 2 to other side

x = -2

the roots are x = 1/2 and -2

2. 3x^2 - 10x - 8 using quadratic formula

a = 3, b = -10, c = -8

x = (-b ± √b² - 4ac)/2a  substitute the value

x = (-(-10) ± √-10² - 4(3)(-8))/2(3) simplify

x = (10) ± √100 +96)/6

x = (10) ± √196)/6 get the square root of 196

x = 10 ± 14/6

when x is positive

x = (10+14)/6 = 24/6 = 4

when x is negative

x = (10-14)/6 = -4/6 = -2/3

the roots are x = 4 and -2/3

3. 4x^2 + 8x + 3 = 0 use factoring

(4x + 1 ) (x + 3) = 0

4x + 1 = 0 transpose 1 to other side

4x = -1 divide both side by 4

x = -1/4

x + 3 = 0 transpose 3 to other side

x = -3

the roots are x = -1/4 and -3