To solve the quadratic equation \(2t^2 - 13t + 21 = 0\), we can use the quadratic formula:

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

where \(a = 2\), \(b = -13\), and \(c = 21\).

1. **Calculate the discriminant**:

\[
b^2 - 4ac = (-13)^2 - 4 \cdot 2 \cdot 21 = 169 - 168 = 1
\]

2. **Use the quadratic formula**:

\[
t = \frac{13 \pm \sqrt{1}}{2 \cdot 2} = \frac{13 \pm 1}{4}
\]

This gives us two solutions:

\[
t_1 = \frac{14}{4} = 3.5 \quad \text{and} \quad t_2 = \frac{12}{4} = 3
\]

Thus, the solutions to the equation \(2t^2 - 13t + 21 = 0\) are:

\[
t = 3.5 \quad \text{and} \quad t = 3
\]

Would you like more details on any part of this process? Here are some related questions you might consider:

1. How do you graph a quadratic function?
2. What are the characteristics of the quadratic formula?
3. Can you explain the significance of the discriminant?
4. How do you factor quadratic equations?
5. What applications do quadratic equations have in real life?

**Tip**: When solving quadratics, always check if the equation can be factored for a quicker solution.

Explore the step-by-step solution for the quadratic equation 2t^2 - 13t + 21 = 0. This guide highlights the use of the quadratic formula and the significance of the discriminant, suitable for students in Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation