Question

Solve (x-2)(2x-1) = 0

Answer 1

In short, to solve the equation (x-2)(2x-1) = 0, we use the zero product property by setting each factor equal to zero and solving for x. The solutions are x = 2 and x = 1/2.

Explanation:

The equation (x-2)(2x-1) = 0 can be solved by finding the values of x that make the left-hand side of the equation equal to zero.

To do this, we can use the zero product property, which states that if the product of two factors is equal to zero, then at least one of the factors must be equal to zero.

Therefore, we set each factor equal to zero and solve for x:

x-2 = 0 or 2x-1 = 0

Solving each equation for x, we get:

x = 2 or x = 1/2

So the solutions to the equation (x-2)(2x-1) = 0 are x = 2 and x = 1/2.

Answer 2

x = 2

x = 1/2

Explanation:

To solve the given equation (x-2)(2x-1) = 0, we need to find the values of 'x' that make the left-hand side of the equation equal to zero. For this, we need to use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

Using the zero product property, we can set each factor equal to zero and solve for 'x'.

First factor: x - 2 = 0

Adding 2 to both sides, we get:

x = 2

Second factor: 2x - 1 = 0

Adding 1 to both sides, we get:

2x = 1

Dividing by 2 on both sides, we get:

x = 1/2

Therefore, the solutions to the given equation (x-2)(2x-1) = 0 are x = 2 and x = 1/2.

We can verify our solutions by plugging them back into the original equation and checking if the left-hand side equals zero.

When x = 2, we have:

(x-2)(2x-1) = (2-2)(2(2)-1) = 0, which is true.

When x = 1/2, we have:

(x-2)(2x-1) = (1/2-2)(2(1/2)-1) = (-3/2)(0) = 0, which is also true.

Therefore, our solutions are correct.

FYI, you could've also multiplied the polynomials to get a quadratic equation, though this is terribly inefficient for this case.