Solve the quadratic equation 3x2−5x+2=0 using the quadratic formula. Please show all your work with the Quad Formula to earn your points. You can upload a photo of your work if you prefer.
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / 2a
Given the quadratic equation 3x^2 - 5x + 2 = 0, we can identify a=3, b=-5, and c=2.
Substitute these values into the quadratic formula:
x = (5 ± √((-5)^2 - 4*3*2)) / (2*3)
x = (5 ± √(25 - 24)) / 6
x = (5 ± √1) / 6
x = (5 ± 1) / 6
Therefore, we have two possible solutions:
x1 = (5 + 1) / 6 = 6 / 6 = 1
x2 = (5 - 1) / 6 = 4 / 6 = 2/3
Therefore, the solutions to the quadratic equation 3x^2 - 5x + 2 = 0 are x = 1 and x = 2/3.