We are given the tasks shown below. We are asked to work them out and find the one that is different.

First of all, let's recall that roots is the way we refer to the solutions of an equation that is set equal to zero. Therefore, to solve and to find the roots of the equation $(2 k + 4) (k - 3) = 0,$ are equivalent things. Now, to solve this equation let's recall the Zero Product Property.

Zero Product Property
If the product of two numbers is $0,$ then at least one of the numbers is $0 .$ \|}

According to the Zero Product Property, for the product $(2 k + 4) (k - 3)$ to be $0$ is either $(2 k + 4) = 0$ or $(k - 3) = 0 .$ Therefore, the task asking to find the values that satisfy these equations is also equivalent to solving $(2 k + 4) (k - 3) = 0 .$ Then, we can already point out which is the different task.

Now, let's continue to find the solutions to the equation

(2 k + 4) (k - 3) = 0 .

(2 k + 4) (k - 3) = 0 Solution 1 2 k + 4 = 0 2 k = - 4 k = - 2 Solution 2 k - 3 = 0 k = 3

As we can see, according to the Zero Product Property the solutions for the equation

(2 k + 4) (k - 3) = 0

are

k = - 2

and

k = 3 .

Finally, the other task is to find the

k - value

for which

(2 k + 4) + (k - 3) = 0 .

(2 k + 4) + (k - 3) = 0

▼

Solve for

k

RemovePar

Remove parentheses

2 k + 4 + k - 3 = 0

AddSubTerms

Add and subtract terms

3 k + 1 = 0

SubEqn

$LHS - 1 = RHS - 1$

3 k = 1

DivEqn

$LHS / 3 = RHS / 3$

k = \frac{1}{3}

Let's summarize our results. The following tasks are equivalent.

Solve the equation $(2 k + 4) (k - 3) = 0 .$
Find the values of $k$ for which $(2 k + 4)$ or $(k - 3) = 0 .$
Find the roots of the equation $(2 k + 4) (k - 3) = 0 .$

The solutions are $k = - 2$ and $k = 3 .$

The task asking to find the value of $k$ for which $(2 k + 4) + (k - 3) = 0$ is the different one. The solution is $k = \frac{1}{3} .$

Exercise