Solve the equation q^2 - 5q + 6 = 0
Understand the Problem
The question asks to solve the quadratic equation. We need to find the values of 'q' that satisfy the equation. This can be done by factoring, completing the square, or using the quadratic formula.
Answer
$q = 2, 3$
Answer for screen readers
$q = 2, 3$
Steps to Solve
- Factor the quadratic equation
We need to find two numbers that multiply to 6 and add up to -5. These numbers are -2 and -3.
- Rewrite the equation using factors
Rewrite the quadratic equation using the factors we found: $$(q - 2)(q - 3) = 0$$
- Solve for q
Set each factor equal to zero and solve for q: $$q - 2 = 0 \implies q = 2$$ $$q - 3 = 0 \implies q = 3$$
$q = 2, 3$
More Information
The quadratic equation $q^2 - 5q + 6 = 0$ has two solutions: $q=2$ and $q=3$.
Tips
A common mistake is to incorrectly factor the quadratic equation, leading to incorrect solutions. For example, choosing the wrong signs or numbers for the factors. Another mistake is only solving for one value of $q$, and forgetting that if a product of terms is equal to zero, then any of the terms can be zero.
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