Question

Solve.5 y³-39 y²}-8 y=0 The solutions are y= (ype an integer or a simplified fraction. Use a comma to separate answers as needed.

Answer 1

The cubic equation .5y³ - 39y² - 8y = 0 needs to be solved by first factoring out the common y and then solving the resulting quadratic equation for further solutions.

Step-by-step explanation:

The student's question asks us to solve the following cubic equation: 0.5y³ - 39y² - 8y = 0. To solve for y, we factored out the common factor, which is y in this case, leading us to y(0.5y² - 39y - 8) = 0.

Next, we set each factor equal to zero:

• y = 0
• 0.5y² - 39y - 8 = 0

Solving the quadratic equation using either factoring, the quadratic formula, or completing the square may provide us with the additional roots.

After solving the quadratic, we'd get the values of y, which represent the solutions to the original equation.