𝒚 = 𝟔x^2− 𝟏𝟗𝒙 + 𝟏0    solución

To solve the quadratic equation \( y = 6x^2 - 19x + 10 \), we can find its **roots** using the **quadratic formula**:

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

For the given equation \( y = 6x^2 - 19x + 10 \), we have:
- \( a = 6 \)
- \( b = -19 \)
- \( c = 10 \)

### Step 1: Calculate the discriminant
The discriminant is the part under the square root in the quadratic formula:

\[
\Delta = b^2 - 4ac
\]

\[
\Delta = (-19)^2 - 4(6)(10) = 361 - 240 = 121
\]

### Step 2: Apply the quadratic formula

\[
x = \frac{-(-19) \pm \sqrt{121}}{2(6)}
\]

\[
x = \frac{19 \pm 11}{12}
\]

### Step 3: Solve for the two roots

- First root: 

\[
x_1 = \frac{19 + 11}{12} = \frac{30}{12} = \frac{5}{2} = 2.5
\]

- Second root:

\[
x_2 = \frac{19 - 11}{12} = \frac{8}{12} = \frac{2}{3}
\]

### Final Solution:
The roots of the quadratic equation are:

\[
x_1 = 2.5 \quad \text{and} \quad x_2 = \frac{2}{3}
\]

Would you like a detailed explanation of the steps or additional help?

Here are 5 related questions:
1. How do you verify the roots of a quadratic equation?
2. What is the importance of the discriminant in quadratic equations?
3. How do you complete the square for this quadratic equation?
4. Can you graph this quadratic function and find the vertex?
5. How does the quadratic formula change for different types of roots?

**Tip**: Always check the discriminant before solving to determine the number and type of solutions.

𝒚 = 𝟔x^2− 𝟏𝟗𝒙 + 𝟏0 solución

Solve the quadratic equation 6x^2 - 19x + 10 step-by-step using the quadratic formula. This solution covers algebraic methods, including the use of the discriminant and calculating roots, suitable for students in Grades 9-12.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation