Need help answering this question? Solve2x^2-3x-2=0 using the quadratic formula?

2x² - 3x - 2 = 0
The quadric equation: r1,r2 = [-b ± √(b² - 4ac)]/2a
r1,r2 = [ 3 ± √((3)² - 4(2)(-2)) ] / (2(2))
r1,r2 = [ 3 ± 5 ] / 4
r1,r2 = 2, -1/2

Answer: x = 2, and x = -1/2

Question Number 1 :
For this equation 2*x^2 - 3*x - 2 = 0 , answer the following questions :
A. Find the roots using Quadratic Formula !

Answer Number 1 :
The equation 2*x^2 - 3*x - 2 = 0 is already in a*x^2+b*x+c=0 form.
So we can imply that the value of a = 2, b = -3, c = -2.

1A. Find the roots using Quadratic Formula !
Use abc formula and you get either
x1 = (-b+sqrt(b^2-4*a*c))/(2*a) or x2 = (-b-sqrt(b^2-4*a*c))/(2*a)
As a = 2, b = -3 and c = -2,
we just need to subtitute the value of a,b and c in the abc formula.
Which produce x1 = (-(-3) + sqrt( (-3)^2 - 4 * (2)*(-2)))/(2*2) and x2 = (-(-3) - sqrt( (-3)^2 - 4 * (2)*(-2)))/(2*2)
Which is the same as x1 = ( 3 + sqrt( 9+16))/(4) and x2 = ( 3 - sqrt( 9+16))/(4)
Which is the same with x1 = ( 3 + sqrt( 25))/(4) and x2 = ( 3 - sqrt( 25))/(4)
So we get x1 = ( 3 + 5 )/(4) and x2 = ( 3 - 5 )/(4)
The answers are x1 = 2 and x2 = -0.5

x = [ 3 ± √ (9 + 16) ] / 4
x = [ 3 ± √ (25) ] / 4
x = [ 3 ± 5 ] / 4
x = 2 , x = - 1/2

Ok so the quadratic equation is ax^2+bx+c=0. In your problem a=2, b= -3, and c= -3. Assuming you know the quadratic formula, plug these numbers in and calculate x. You should have two possible answers for x because of the plus or minus in the quadratic formula. After I plugged the numbers in I got x=2 and x= -1/2 as the two answers. Remember order of operations when you plug those numbers in and you should be OK.

Quadratic formula is

For ax^2 + bx + c = 0

x = (-b + SQRT(b^2 - 4ac) ) / 2a and x = (-b - SQRT(b^2 - 4ac) ) / 2a

Since you have 2x^2 - 3x - 2 = 0
a = 2
b = -3
c = -2

Plugging in the numbers you get x = -1/2 and x = 2

You asked about the quadratic formula, so I'll show you that method.

Look at your equation and compare it to:
ax² + bx + c = 0
2x² -3x - 2 = 0

You can easily figure out the coefficients a, b and c:
a = 2
b = -3
c = -2

The quadratic formula is:
x = (-b ± √(b² - 4ac)) / 2a

Plug in your values:
x = (3 ± √((-3)² - 4(2)(-2))) / 2(2)
x = (3 ± √(9 - (-16)))) / 4
x = (3 ± √25) / 4
x = (3 ± 5) / 4

x = 8/4 = 2
or
x = -2/4 = -1/2

Answer:
x = -1/2 or x = 2

2x^2 - 3x - 2 = 0
x = [-b ±√(b^2 - 4ac)]/2a

a = 2
b = -3
c = -2

x = [3 ±√(9 + 16)]/4
x = [3 ±√25]/4
x = [3 ±5]/4

x = [3 + 5]/4
x = 8/4
x = 2

x = [3 - 5]/4
x = -2/4
x = -1/2 (-0.5)

∴ x = -1/2 (-0.5) , 2