Use a calculator and the quadratic formula to find approximate solutions of the equation.
4.96 x squared minus 10.85 x plus 4.49equals0

To solve the quadratic equation \(4.96x^2 - 10.85x + 4.49 = 0\), we'll use the quadratic formula:

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

where \(a = 4.96\), \(b = -10.85\), and \(c = 4.49\).

### Step 1: Calculate the discriminant
The discriminant is given by \(b^2 - 4ac\):

\[
b^2 = (-10.85)^2 = 117.7225
\]
\[
4ac = 4 \times 4.96 \times 4.49 = 89.1712
\]

Thus, the discriminant is:

\[
117.7225 - 89.1712 = 28.5513
\]

### Step 2: Apply the quadratic formula
Now, calculate the two solutions using:

\[
x = \frac{-(-10.85) \pm \sqrt{28.5513}}{2 \times 4.96}
\]

This simplifies to:

\[
x = \frac{10.85 \pm \sqrt{28.5513}}{9.92}
\]

### Step 3: Compute the solutions
1. \(\sqrt{28.5513} \approx 5.344\)
   
   - Positive solution: \(x_1 = \frac{10.85 + 5.344}{9.92} \approx \frac{16.194}{9.92} \approx 1.633\)
   - Negative solution: \(x_2 = \frac{10.85 - 5.344}{9.92} \approx \frac{5.506}{9.92} \approx 0.555\)

### Approximate solutions
The solutions are approximately:
\[
x_1 \approx 1.633, \quad x_2 \approx 0.555
\]

Would you like more details on the steps? Here are five related questions to expand your understanding:

1. How does the discriminant determine the nature of the solutions?
2. What happens if the discriminant is negative?
3. Can the quadratic formula be used for equations with non-integer coefficients?
4. How would you solve a quadratic equation if the coefficient of \(x^2\) were zero?
5. Why does the quadratic formula always give real or complex solutions?

**Tip:** Always check the discriminant before applying the quadratic formula. It indicates whether the solutions are real or complex.

Use a calculator and the quadratic formula to find approximate solutions of the equation 4.96x^2 - 10.85x + 4.49 = 0.

Learn how to solve the quadratic equation 4.96x^2 - 10.85x + 4.49 = 0 using the quadratic formula. This step-by-step solution covers key algebraic concepts, including calculating the discriminant and applying the quadratic formula. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation