Question

2x² - 10x = 0
what are the solutions to this equation?
○ x = 10 and x = 0
○ x = 0 and x = 5
○ x = 5 only
○ x = 2 and x = 5
○ x = 5 and x = 10

Explanation:

Step1: Factor the equation

Factor out the greatest common factor, which is \(2x\), from the left - hand side of the equation \(2x^{2}-10x = 0\).
We know that \(2x^{2}-10x=2x(x - 5)\), so the equation becomes \(2x(x - 5)=0\).

Step2: Apply the zero - product property

The zero - product property states that if \(ab = 0\), then either \(a = 0\) or \(b = 0\) (or both).
For the equation \(2x(x - 5)=0\), we have two cases:
Case 1: \(2x=0\)
Divide both sides of the equation \(2x = 0\) by 2. We get \(x=\frac{0}{2}=0\).
Case 2: \(x - 5=0\)
Add 5 to both sides of the equation \(x - 5=0\). We get \(x=5\).

Answer:

\(x = 0\) and \(x = 5\) (corresponding to the option: \(x = 0\) and \(x = 5\))