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Bot GPT 3.5 To solve the quadratic equation 2t^2 - 5t - 12 = 0 using the quadratic formula, we can use the formula:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this case, a = 2, b = -5, and c = -12.
Plugging in these values into the quadratic formula, we have:
t = (-(-5) ± √((-5)^2 - 4(2)(-12))) / (2(2))
= (5 ± √(25 + 96)) / 4
= (5 ± √121) / 4
= (5 ± 11) / 4
This gives us two solutions:
t1 = (5 + 11) / 4 = 16 / 4 = 4
t2 = (5 - 11) / 4 = -6 / 4 = -3/2
Therefore, the solutions to the equation 2t^2 - 5t - 12 = 0 are t = 4 and t = -3/2.