Solve the Quadratic Equation: x²-6x+8=0 for Parameter x

Q: How do I know which two numbers to choose for factoring?

Look for two numbers that multiply to give you the constant term (8) and add to give you the middle coefficient (-6). For this problem, -2 × -4 = 8 and -2 + (-4) = -6.

Q: Why do we set each factor equal to zero?

This uses the Zero Product Property: if two things multiply to equal zero, then at least one of them must be zero. So if $ (x-2)(x-4) = 0 $, then either x-2 = 0 or x-4 = 0.

Q: How can I check my factoring is correct?

Expand your factored form back out using FOIL. $ (x-2)(x-4) = x^2 - 4x - 2x + 8 = x^2 - 6x + 8 $. If it matches the original equation, you're right!

Q: Can a quadratic have more than two solutions?

No! A quadratic equation can have at most two real solutions. This is because the highest power is 2, which means the parabola can cross the x-axis at most twice.

Quadratic Equations with Factoring Method

Find the value of the parameter x.

$x^2-6x+8=0$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 We will use a trinomial to find the solution

00:06 Find two numbers whose sum equals value B

00:09 and their product equals value C

00:14 These are the matching numbers

00:19 Let's substitute these numbers in the trinomial

00:24 Find what zeros each factor

00:27 Isolate the unknown, this is one solution, now let's find the second

00:34 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Find the value of the parameter x.

$x^2-6x+8=0$

Step-by-step solution

To solve this quadratic equation by factoring, follow these steps:

Step 1: Write the equation: $x^2 - 6x + 8 = 0$ .
Step 2: Find two numbers that multiply to $+8$ (the constant term) and add up to $-6$ (the coefficient of $x$ ).

These numbers are $-2$ and $-4$ , since $(-2) \times (-4) = 8$ and $(-2) + (-4) = -6$ .

Step 3: Rewrite the quadratic expression as $(x - 2)(x - 4) = 0$ .
Step 4: Solve each factor separately:
- $x - 2 = 0 \Rightarrow x = 2$
- $x - 4 = 0 \Rightarrow x = 4$

Therefore, the solutions to the quadratic equation $x^2 - 6x + 8 = 0$ are $x = 2$ and $x = 4$ .

The correct choice for the solution is:

$x=2,x=4$ which corresponds to choice 4.

Final Answer

$x=2,x=4$

Key Points to Remember

Essential concepts to master this topic

Factoring Rule: Find two numbers that multiply to c and add to b
Technique: For $x^2 - 6x + 8$ , use -2 and -4 since (-2)(-4) = 8
Check: Substitute x = 2: $(2)^2 - 6(2) + 8 = 0$ ✓

Common Mistakes

Avoid these frequent errors

Finding numbers that add to +6 instead of -6
Don't look for numbers adding to +6 when the coefficient is -6x = wrong factors! This gives solutions like x = -2 and x = -4 instead of the correct x = 2 and x = 4. Always match the sign of the middle term coefficient exactly.

Practice Quiz

Test your knowledge with interactive questions

Find the value of the parameter x.

$$ x^2-6x+8=0 $$

FAQ

Everything you need to know about this question

How do I know which two numbers to choose for factoring?

Look for two numbers that multiply to give you the constant term (8) and add to give you the middle coefficient (-6). For this problem, -2 × -4 = 8 and -2 + (-4) = -6.

Why do we set each factor equal to zero?

This uses the Zero Product Property: if two things multiply to equal zero, then at least one of them must be zero. So if $(x-2)(x-4) = 0$ , then either x-2 = 0 or x-4 = 0.

What if the quadratic doesn't factor nicely?

Not all quadratics can be factored with nice integer solutions! If factoring seems impossible, you can use the quadratic formula or completing the square instead.

How can I check my factoring is correct?

Expand your factored form back out using FOIL. $(x-2)(x-4) = x^2 - 4x - 2x + 8 = x^2 - 6x + 8$ . If it matches the original equation, you're right!

Can a quadratic have more than two solutions?

No! A quadratic equation can have at most two real solutions. This is because the highest power is 2, which means the parabola can cross the x-axis at most twice.

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Solve the Quadratic Equation: x²-6x+8=0 for Parameter x

Quadratic Equations with Factoring Method

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

How do I know which two numbers to choose for factoring?

Why do we set each factor equal to zero?

What if the quadratic doesn't factor nicely?

How can I check my factoring is correct?

Can a quadratic have more than two solutions?

🌟 Unlock Your Math Potential

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