Solving the Quadratic Equation 2x^2 - 5x = 0

Question

Solve: 2x^2 −5x=0 The solutions are:

A) x=0

B) x=0,x=5 C) x=0,x=–5

D) x=0,x=52

Answer 1

Answer 2

^{Here’s a detailed step-by-step solution for the quadratic equation:}

^{Given equation:}

^{2x2−5x=0 2x^2 - 5x = 0 2x2−5x=0}

^{Step 1: Factor the equation}

^{Look for common factors in both terms. Both terms have xxx as a common factor:}

^{x(2x−5)=0x(2x - 5) = 0x(2x−5)=0}

^{Step 2: Apply the Zero Product Property}

^{The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero. So, set each factor equal to zero:}

1. ^{First factor:}
2. ^{x=0x = 0x=0Second factor:}

^{2x−5=0 2x - 5 = 0 2x−5=0}

^{Step 3: Solve each equation}

1. ^{For x=0x = 0x=0, this is already solved.}
2. ^{For 2x−5=02x - 5 = 02x−5=0:}
3. ^{Add 5 to both sides:}

^{2x=52x = 52x=5Now divide both sides by 2:}

^{x=52x = \frac{5}{2}x=25​}

^{Step 4: Write the final answer}

^{The two solutions are:}

^{x=0andx=52x = 0 \quad \text{and} \quad x = \frac{5}{2}x=0andx=25}

^{​Final Answer:}

^{The correct option is D) x=0,x=52x = 0, x = \frac{5}{2}x=0,x=25​.}

Answer 3

To solve for x, we need to do some factoring. Factoring is the process of breaking down expression into a product of simpler expressions or factors.

2x^2 - 5x = 0

x(2x-5) = 0

now take the two products and split them up and set each one equal to zero

x = 0

2x - 5 = 0. x = 5/2

therefore, the overall solutions are X equals zero and X equals 5/2. You can verify these by putting them back into the original equation to see if the equation is true.

Answer 4

We are solving the quadratic equation:

$$

2x^2 - 5x = 0.

$$

### Step 1: Factorize the equation

Factor out the common term $x$ from both terms:

$$

x(2x - 5) = 0.

$$

### Step 2: Apply the zero-product property

The zero-product property states that if the product of two factors is zero, then at least one of the factors must be zero. Therefore:

$$

x = 0 \quad \text{or} \quad 2x - 5 = 0.

$$

### Step 3: Solve each factor

1. From $x = 0$, we already have one solution:

$$

x = 0.

$$

2. Solve $2x - 5 = 0$ for $x$:

$$

2x = 5,

$$

$$

x = \frac{5}{2}.

$$

### Step 4: Combine the solutions

The solutions to the equation are:

$$

x = 0 \quad \text{and} \quad x = \frac{5}{2}.

$$

### Final Answer:

$$

\boxed{D \, x = 0, x = \frac{5}{2}}

$$x=0andx=25​.

Answer 5