What are the solutions to the quadratic equation X squared = 5X?

What are the solutions to the quadratic equation X squared = 5X?

• A. 5, 0
• B. 0, 1
• C. 0, 5
• D. 1, 5

Answer: (C)

To solve the quadratic equation \(X^2 = 5X\), we first rearrange the equation into standard form. Subtracting \(5X\) from both sides gives us: \[ X^2 - 5X = 0 \] Next, we can factor out an \(X\) from the left side: \[ X(X - 5) = 0 \] Setting each factor equal to zero results in the possible solutions: 1. \(X = 0\) 2. \(X - 5 = 0 \implies X = 5\) Therefore, the solutions to the equation are \(0\) and \(5\). This aligns with the response indicating that the solutions are \(0\) and \(5\). The quadratic has two distinct solutions, which is a characteristic feature, showing that it has crossed the x-axis at these points. This confirms that the correct answer encapsulates both roots derived from the factored form.

To solve the quadratic equation (X^2 = 5X), we first rearrange the equation into standard form. Subtracting (5X) from both sides gives us:

[

X^2 - 5X = 0

]

Next, we can factor out an (X) from the left side:

[

X(X - 5) = 0

]

Setting each factor equal to zero results in the possible solutions:

1. (X = 0)

2. (X - 5 = 0 \implies X = 5)

Therefore, the solutions to the equation are (0) and (5).

This aligns with the response indicating that the solutions are (0) and (5). The quadratic has two distinct solutions, which is a characteristic feature, showing that it has crossed the x-axis at these points. This confirms that the correct answer encapsulates both roots derived from the factored form.