Question
QUESTION 1 1.1 Solve for \( x \) in each of the following: 1.1.1 \( \quad 2 x(x-3)=0 \)
Ask by Munoz Powers. in South Africa
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The solutions are \( x=0 \) and \( x=3 \).
Solution
Solve the equation \( 2x(x-3)=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(2x\left(x-3\right)=0\)
- step1: Divide the terms:
\(x\left(x-3\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&x-3=0\\&x=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&x=3\\&x=0\end{align}\)
- step4: Rewrite:
\(x_{1}=0,x_{2}=3\)
The solutions to the equation \(2x(x-3)=0\) are \(x=0\) and \(x=3\).
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Simplify this solution Bonus Knowledge
To solve the equation \( 2x(x-3)=0 \), we can use the zero product property, which states that if a product of factors equals zero, at least one of the factors must be zero. Here, we have two factors: \( 2x \) and \( (x-3) \). Setting each factor to zero gives us the possible solutions: 1. **For \( 2x = 0 \)**: Dividing by 2, we get \( x = 0 \). 2. **For \( x - 3 = 0 \)**: Adding 3 to both sides, we get \( x = 3 \). Thus, the solutions for \( x \) are \( x = 0 \) and \( x = 3 \). Just like that, you’ve learned an efficient method to solve quadratic equations by factoring! Who knew equations could be so helpful in unveiling the mysteries of math?
