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Las soluciones son \(x=0\) o \(x=2\).
Solución
Solve the equation \( 3x^{2}-6x=0 \).
Solve the quadratic equation by following steps:
- step0: Solve by factoring:
\(3x^{2}-6x=0\)
- step1: Factor the expression:
\(3x\left(x-2\right)=0\)
- step2: Separate into possible cases:
\(\begin{align}&x-2=0\\&3x=0\end{align}\)
- step3: Solve the equation:
\(\begin{align}&x=2\\&x=0\end{align}\)
- step4: Rewrite:
\(x_{1}=0,x_{2}=2\)
La solución de la ecuación \(3x^{2}-6x=0\) es \(x=0\) o \(x=2\).
Respondido por UpStudy AI y revisado por un tutor profesional
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Simplifique esta solución Bonus Knowledge
Did you know this equation can be factored easily? You can start by taking out the common factor of \(3x\), giving you the expression \(3x(x - 2) = 0\). From there, you can use the zero product property to find the solutions: set each factor equal to zero. This reveals your roots as \(x = 0\) and \(x = 2\)! In practical terms, equations like this pop up all the time in fields like physics and engineering. For example, if you're calculating the trajectory of a projectile, the motion equations may just take the form of a quadratic equation similar to this one! Finding the roots helps determine critical points, like when it hits the ground.
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