Question

Solve the equation 45−6d³−5d²=0 for d.
a)d=−3
b)d=1
c)d=−1
d)d=3

Answer 1

Upon substituting the given options into the cubic equation, none of them satisfy the equation. A different approach, such as factoring or using a cubic formula, is necessary to find the correct solution.

Step-by-step explanation:

To solve the equation 45−6d³−5d²=0 for d, we can start by rearranging it in descending powers of d as -6d³ - 5d² + 45 = 0.

Factoring out common terms or using polynomial division is a common approach to solve such cubic equations. However, upon reviewing the given options, we can start by simple substitution to verify if any of the provided options are indeed the solutions to the equation.

1. Substitute d = -3: -6(-3)³ - 5(-3)² + 45 = 0, simplifying to -162 + 45 + 45 = 0, which equals -72 and therefore is not equal to zero.
2. Substitute d = 1: -6(1)³ - 5(1)² + 45 = 0, simplifying to -6 - 5 + 45 = 0, which equals 34 and hence is not zero.
3. Substitute d = -1: -6(-1)³ - 5(-1)² + 45 = 0, simplifying to 6 - 5 + 45 = 0, which equals 46 and is not zero.
4. Substitute d = 3: -6(3)³ - 5(3)² + 45 = 0, simplifying to -162 - 45 + 45 = 0, which simplifies to -162 and thus is not zero.

None of the provided options is the correct solution to the equation. Therefore, the correct answer requires a different, more systematic approach to solving, such as factoring or applying the cubic formula, if it exists.