Final answer:
To find the roots of the quadratic equation -4.9t² + 27.5t + 9, we can use the quadratic formula. The roots are approximately -0.98 and 5.63.
Step-by-step explanation:
The given expression is a quadratic equation of the form -4.9t²+27.5t+9. To find the roots of the equation, we can use the quadratic formula:
t = (-b ± √(b² - 4ac)) / (2a)
Substituting the values of a = -4.9, b = 27.5, and c = 9 into the formula, we get:
t = (-27.5 ± √(27.5² - 4(-4.9)(9))) / (2(-4.9))
Simplifying further, we have:
t = (-27.5 ± √1739.75) / -9.8
Hence, the roots of the given quadratic equation are approximately -0.98 and 5.63.