Now solve 6x2−17x+12 =0 for x using the quadratic formula. Remember to show your work.
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The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation 6x^2 - 17x + 12 = 0, we have:
a = 6
b = -17
c = 12
Plugging these values into the quadratic formula, we get:
x = (-(-17) ± √((-17)^2 - 4*6*12)) / (2*6)
This simplifies to:
x = (17 ± √(289 - 288)) / 12
x = (17 ± √1) / 12
Since √1 = 1, we further simplify to:
x = (17 ± 1) / 12
This leads to two possible solutions:
1. x = (17 + 1) / 12 = 18 / 12 = 3/2
2. x = (17 - 1) / 12 = 16 / 12 = 4/3
Therefore, the solutions to the equation 6x^2 - 17x + 12 = 0 are x = 3/2 and x = 4/3.