Answer:
Explanation:
The equation 25d^3 + 210d^2 - 640 = 0 can be reduced to a quadratic equation by using the factor theorem:
(d - 8)(25d^2 + 182d + 80) = 0
So, one root of the equation is d = 8. To find the other two roots, you can solve the quadratic equation:
25d^2 + 182d + 80 = 0
Using the quadratic formula, the roots can be calculated as:
d = (-b ± √(b^2 - 4ac)) / 2a
Where a = 25, b = 182, and c = 80.
So,
d = (-182 ± √(182^2 - 4 * 25 * 80)) / 2 * 25
d = (-182 ± √(33124 - 8000)) / 50
d = (-182 ± √(25124)) / 50
d = (-182 ± 158) / 50
Therefore, the roots of the equation are:
d = (-340 + 158) / 50 = (-182 + 158) / 50 = (-24) / 50 = -0.48
d = (-340 - 158) / 50 = (-182 - 158) / 50 = -340 / 50 = -6.8
So, the solutions to the equation are d = 8, -0.48, and -6.8.