Solve the equation in different ways: x^2 - 3x + 2 = 0.
Understand the Problem
The question is asking to solve the quadratic equation x^2 - 3x + 2 = 0 using different methods, which may include factoring, using the quadratic formula, or completing the square.
Answer
The solutions are $x = 1$ and $x = 2$.
Answer for screen readers
The solutions to the equation $x^2 - 3x + 2 = 0$ are $x = 1$ and $x = 2$.
Steps to Solve
- Identify the quadratic equation form
The given equation is in the standard form of a quadratic equation, which is $ax^2 + bx + c = 0$. Here, $a = 1$, $b = -3$, and $c = 2$.
- Factoring the quadratic equation
To factor the equation $x^2 - 3x + 2 = 0$, we need to find two numbers that multiply to $c(2)$ and add to $b(-3)$. The numbers are $-1$ and $-2$ since:
$$ -1 \times -2 = 2 $$
and
$$ -1 + -2 = -3 $$
Thus, we can write the equation as:
$$(x - 1)(x - 2) = 0$$
- Setting each factor to zero
Now, we can set each factor equal to zero:
$$ x - 1 = 0 \quad \text{or} \quad x - 2 = 0 $$
- Solving for x
Solve each equation for $x$:
From $x - 1 = 0$, we get:
$$ x = 1 $$
From $x - 2 = 0$, we get:
$$ x = 2 $$
- Final solutions
The solutions to the equation $x^2 - 3x + 2 = 0$ are:
$$ x = 1 \quad \text{and} \quad x = 2 $$
The solutions to the equation $x^2 - 3x + 2 = 0$ are $x = 1$ and $x = 2$.
More Information
Factoring a quadratic equation is one of the simplest methods for finding its roots, especially when the coefficients are small integers. If factoring doesn't work easily, other methods like the quadratic formula or completing the square can be used as alternatives.
Tips
- Forgetting to set each factor to zero; some students may skip this key step.
- Mixing up the signs when adding or multiplying; be cautious with negative numbers.
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