Question

In the given equation, b is a positive constant.

The sum of the solutions of the equation is 5.
What is the value of b?
x²(x+3)(x - b) = 0

Answer 1

Answer: b = 8

Explanation:

From the equation, we can see that x = 0 is one of the solutions. This means that the remaining solutions must add up to 5.

Let's factor the equation and set each factor equal to zero:

x²(x+3)(x - b) = 0

x = 0 or x + 3 = 0 or x - b = 0

Solving for x in each case, we get:

x = 0 or x = -3 or x = b

Since the sum of the solutions is 5, we can write:

0 + (-3) + b = 5

Simplifying, we get:

b - 3 = 5

Adding 3 to both sides, we get:

b = 8

Therefore, the value of b is 8.

Answer 2

Answer:

b = 8.

Step by step solved:

Since the equation is equal to zero, it can be factored into three parts: x²=0, x+3=0, and x-b=0.

The solutions for x²=0 are x=0 and x=0 (a double root).

The solution for x+3=0 is x=-3.

The solution for x-b=0 is x=b.

Therefore, the sum of the solutions is 0 + 0 + (-3) + b = 5.

Simplifying the equation, we get b = 8.

So the value of b is 8.