Question:
What is the solution to the equation \( x^2 - 5x + 6 = 0 \)?
What is the solution to the equation \( x^2 - 5x + 6 = 0 \)?
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For multiple-choice questions involving equations, you can quickly check the answers by substituting the given option values back into the equation. For example, for option (B), plugging in x=2 gives \( (2)^2 - 5(2) + 6 = 4 - 10 + 6 = 0 \), which is correct. Plugging in x=3 gives \( (3)^2 - 5(3) + 6 = 9 - 15 + 6 = 0 \), which is also correct.
Updated On: Oct 4, 2025
- 1 and 6
- 2 and 3
- -2 and -3
- 1 and 2
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the Concept:
This is a quadratic equation of the form \( ax^2 + bx + c = 0 \). We can solve it by factoring, which involves finding two numbers that multiply to 'c' and add up to 'b'.
Step 2: Detailed Explanation:
The given equation is \( x^2 - 5x + 6 = 0 \).
Here, \( a=1 \), \( b=-5 \), and \( c=6 \).
We need to find two numbers that:
Multiply to \( c = 6 \)
Add to \( b = -5 \)
Let's consider the factors of 6: (1, 6), (2, 3), (-1, -6), (-2, -3).
Now let's check their sums:
\( 1 + 6 = 7 \)
\( 2 + 3 = 5 \)
\( -1 + (-6) = -7 \)
\( -2 + (-3) = -5 \)
The pair that satisfies both conditions is -2 and -3.
So, we can factor the equation as:
\[ (x - 2)(x - 3) = 0 \] For this product to be zero, at least one of the factors must be zero.
\[ \text{Either } x - 2 = 0
\text{or}
x - 3 = 0 \] Solving for x in each case:
\[ x = 2
\text{or}
x = 3 \] Step 3: Final Answer:
The solutions to the equation are 2 and 3.
This is a quadratic equation of the form \( ax^2 + bx + c = 0 \). We can solve it by factoring, which involves finding two numbers that multiply to 'c' and add up to 'b'.
Step 2: Detailed Explanation:
The given equation is \( x^2 - 5x + 6 = 0 \).
Here, \( a=1 \), \( b=-5 \), and \( c=6 \).
We need to find two numbers that:
Multiply to \( c = 6 \)
Add to \( b = -5 \)
Let's consider the factors of 6: (1, 6), (2, 3), (-1, -6), (-2, -3).
Now let's check their sums:
\( 1 + 6 = 7 \)
\( 2 + 3 = 5 \)
\( -1 + (-6) = -7 \)
\( -2 + (-3) = -5 \)
The pair that satisfies both conditions is -2 and -3.
So, we can factor the equation as:
\[ (x - 2)(x - 3) = 0 \] For this product to be zero, at least one of the factors must be zero.
\[ \text{Either } x - 2 = 0
\text{or}
x - 3 = 0 \] Solving for x in each case:
\[ x = 2
\text{or}
x = 3 \] Step 3: Final Answer:
The solutions to the equation are 2 and 3.
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