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What are the solutions of the equation x4 – 5×2 – 36 = 0? use factoring to solve.

What are the solutions of the equation x4 – 5×2 – 36 = 0? use factoring to solve.

The Correct Answer is

Correct Answer Explanation:

Let’s solve the given quadratic equation using factoring.

Step 1: Recognizing the Quadratic Form

Notice that this equation is in quadratic form, meaning we can represent it as .

Step 2: Factoring

Now, let’s introduce a substitution to make this equation easier to factor. Let , so our equation becomes .

Now, we need to factor the quadratic expression . We are looking for two numbers whose product is −36×1 (coefficient of ) and whose sum is (coefficient of ).

The numbers that satisfy this condition are and because and .

So, we can express as .

Step 3: Substitute Back

Now, substitute back for : .

Now, we have a product of two factors equal to zero. According to the zero-product property, this implies that either or .

Solving for :

Add 9 to both sides:

Take the square root of both sides:

Solving for :

Subtract 4 from both sides:

This has no real solutions because the square of any real number is non-negative, and here we’re looking for a square to be .

The solutions to the original equation are , based on the solutions obtained from .

Why the other solutions are  Incorrect:

b. Incorrect Solution:

This solution is incorrect because it does not satisfy the original equation . If we substitute or into the original equation, we get or , neither of which equals zero.

c.  Incorrect Solution:

Similarly, this solution is incorrect. Substituting or into the original equation results in or , which are not equal to zero.

d.  Incorrect Solution:

This solution is also incorrect. When substituting into the original equation, we get , which is not equal to zero.

All the incorrect solutions were evaluated by substituting them into the original equation , and in each case, the equation did not hold true. Therefore, the correct solutions are , and the incorrect solutions are and , and .

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