Given is the equation 4.8x2 + 36.8x + 3.9 = 0. What is the smallest root of this equation?

The given quadratic equation is:

\[
4.8x^2 + 36.8x + 3.9 = 0
\]

To find the roots of the quadratic equation, we use the quadratic formula:

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

Here, \( a = 4.8 \), \( b = 36.8 \), and \( c = 3.9 \). Let's substitute these values into the formula.

### Step-by-Step Calculation:

\[
x = \frac{-36.8 \pm \sqrt{(36.8)^2 - 4(4.8)(3.9)}}{2(4.8)}
\]

Now I'll compute the values.

The two roots of the quadratic equation \( 4.8x^2 + 36.8x + 3.9 = 0 \) are approximately:

\[
x_1 = -0.1075 \quad \text{and} \quad x_2 = -7.5592
\]

The smallest root is \( x_2 = -7.5592 \).

Would you like more details on the calculation, or have any other questions?

Here are some related questions to explore:
1. How is the discriminant used to determine the nature of the roots?
2. What is the significance of the quadratic formula in solving equations?
3. How would the roots change if the coefficients of the equation were altered?
4. What is the graphical interpretation of the roots of a quadratic equation?
5. How can we verify the roots of the quadratic equation manually?

**Tip:** For any quadratic equation, if the discriminant (\(b^2 - 4ac\)) is positive, the roots will be real and distinct.

Given is the equation 4.8x^2 + 36.8x + 3.9 = 0. What is the smallest root of this equation?

Discover how to solve the quadratic equation 4.8x^2 + 36.8x + 3.9 using the quadratic formula. Learn step-by-step how to compute the smallest root of the equation, with key concepts in algebra and quadratic equations. Suitable for students in Grades 9-12.

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