Quadratic equation for 3x²-4x=0 using this steps

Step1.Determine the values of a.b and c.

Step2.Substitute the values of a band c in the quadratic formula.

Step3.Solve to find the solutions.

Step4.Application of the Steps

Step5.Check by substituting each solution in the original equation

Let's solve the quadratic equation \( 3x^2 - 4x = 0 \) using the steps you provided.

### Step 1: Determine the values of \( a \), \( b \), and \( c \).

The general form of a quadratic equation is:

\[
ax^2 + bx + c = 0
\]

For the given equation \( 3x^2 - 4x = 0 \), we can identify:

- \( a = 3 \) (coefficient of \( x^2 \))
- \( b = -4 \) (coefficient of \( x \))
- \( c = 0 \) (constant term)

### Step 2: Substitute the values of \( a \), \( b \), and \( c \) into the quadratic formula.

The quadratic formula is:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Substituting \( a = 3 \), \( b = -4 \), and \( c = 0 \):

\[
x = \frac{-(-4) \pm \sqrt{(-4)^2 - 4(3)(0)}}{2(3)}
\]

### Step 3: Solve to find the solutions.

Let's simplify the equation:

\[
x = \frac{4 \pm \sqrt{16 - 0}}{6}
\]
\[
x = \frac{4 \pm \sqrt{16}}{6}
\]
\[
x = \frac{4 \pm 4}{6}
\]

Now, calculate the two possible values for \( x \):

1. \( x_1 = \frac{4 + 4}{6} = \frac{8}{6} = \frac{4}{3} \)
2. \( x_2 = \frac{4 - 4}{6} = \frac{0}{6} = 0 \)

So, the solutions are \( x_1 = \frac{4}{3} \) and \( x_2 = 0 \).

### Step 4: Application of the steps.

We have applied the quadratic formula and found the solutions:

- \( x_1 = \frac{4}{3} \)
- \( x_2 = 0 \)

### Step 5: Check by substituting each solution into the original equation.

We substitute \( x = \frac{4}{3} \) and \( x = 0 \) back into the original equation \( 3x^2 - 4x = 0 \) to verify.

1. **For \( x = \frac{4}{3} \):**

\[
3 \left(\frac{4}{3}\right)^2 - 4\left(\frac{4}{3}\right) = 3\left(\frac{16}{9}\right) - 4\left(\frac{4}{3}\right) = \frac{48}{9} - \frac{16}{3} = \frac{48}{9} - \frac{48}{9} = 0
\]

This checks out.

2. **For \( x = 0 \):**

\[
3(0)^2 - 4(0) = 0
\]

This also checks out.

Thus, the solutions are correct.

---

Would you like more details on any step or have further questions?

Here are 5 related questions to expand your understanding:
1. How would you solve a quadratic equation that doesn't have a zero constant term?
2. What is the discriminant, and how does it affect the nature of the solutions in a quadratic equation?
3. Can you graph the quadratic function \( 3x^2 - 4x \) and identify the solutions visually?
4. What happens if the discriminant is negative, and how do we handle complex solutions?
5. How can the quadratic formula be derived from completing the square?

**Tip**: Always check the discriminant \( b^2 - 4ac \) before solving a quadratic equation, as it tells you whether the solutions are real or complex.

Quadratic equation for 3x² - 4x = 0 using these steps: 1. Determine the values of a, b, and c. 2. Substitute the values of a, b, and c in the quadratic formula. 3. Solve to find the solutions. 4. Application of the Steps. 5. Check by substituting each solution in the original equation.

Step-by-step solution for solving the quadratic equation 3x² - 4x = 0. This solution explains how to determine the values of a, b, and c, substitute them into the quadratic formula, and find the solutions. Suitable for students in Grades 8-10 studying algebra and quadratic equations.

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