Question

Please solve the question. Thank you.

Answer 1

The solutions to the quadratic equation
`\(16t^2 - 16t - 41 = 0\)` are
`\(t_1 \approx -0.787\)` and
`\(t_2 \approx 2.537\)`.

To solve the quadratic equation
`\(16t^2 - 16t - 41 = 0\)`, we can use the quadratic formula:

`\[ t = (-b \pm √(b^2 - 4ac))/(2a) \]`

Here, a = 16, b = -16, and c = -41. Plugging these values into the formula:

`\[ t = (-(-16) \pm √((-16)^2 - 4(16)(-41)))/(2(16)) \]`

Simplifying further:

`\[ t = (16 \pm √(256 + 2624))/(32) \]\[ t = (16 \pm √(2880))/(32) \]\[ t = (16 \pm 8√(10))/(32) \]\[ t = (1 \pm √(10))/(4) \]`

So, the two solutions are:

`\[ t_1 = (1 - √(10))/(4) \approx -0.787 \]\[ t_2 = (1 + √(10))/(4) \approx 2.537 \]`

These are the simplified radical forms of the solutions.