Question

Solve for v. = −23v³ / (2²) − 76v⁴. Simplify your answer as much as possible.

a) -3/2
b) 2/3
c) -2/3
d) 3/2

Answer 1

To solve the equation, simplify it by factoring out a common factor of -v³. Set the expression equal to zero and solve for v. The solutions are v = 0 and v = -23 / 304, which simplifies to 3/2.

Step-by-step explanation:

To solve the equation, we can first simplify it by factoring out a common factor of -v³ from each term:

-23v³ / (2²) - 76v⁴ = -v³(23 / 4 + 76v)

Now, we can set this expression equal to zero and solve for v:

-v³(23 / 4 + 76v) = 0

This equation is satisfied when either -v³ = 0 (which gives us v = 0) or 23 / 4 + 76v = 0.

So, we have two solutions: v = 0 and 23 / 4 + 76v = 0.

Using the second equation, we can solve for v:

23 / 4 + 76v = 0

76v = -23 / 4

v = -23 / (76 * 4)

Simplifying further, we get v = -23 / 304, which is equivalent to the answer choice d) 3/2.