If a < 1. and 2a^2 - 7a +3= 0, what is the value of a?  could you please solve this equation and create similar exercises 

We are given the quadratic equation:

\[
2a^2 - 7a + 3 = 0
\]

To solve this equation, we will use the quadratic formula, which is given by:

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

For the equation \( 2a^2 - 7a + 3 = 0 \), we can identify the coefficients:
- \( A = 2 \)
- \( B = -7 \)
- \( C = 3 \)

Now, let's substitute these values into the quadratic formula:

\[
a = \frac{-(-7) \pm \sqrt{(-7)^2 - 4(2)(3)}}{2(2)}
\]

Simplifying step by step:

\[
a = \frac{7 \pm \sqrt{49 - 24}}{4}
\]

\[
a = \frac{7 \pm \sqrt{25}}{4}
\]

\[
a = \frac{7 \pm 5}{4}
\]

So, we have two possible solutions:

1. \( a = \frac{7 + 5}{4} = \frac{12}{4} = 3 \)
2. \( a = \frac{7 - 5}{4} = \frac{2}{4} = 0.5 \)

Since we are given that \( a < 1 \), the correct value is:

\[
a = 0.5
\]

### Similar Exercises:
Here are five similar quadratic equations you can solve:

1. \( 3x^2 - 8x + 4 = 0 \) where \( x < 1 \)
2. \( 4y^2 - 5y + 1 = 0 \) where \( y < 1 \)
3. \( 5z^2 - 9z + 2 = 0 \) where \( z < 1 \)
4. \( 6b^2 - 11b + 4 = 0 \) where \( b < 1 \)
5. \( 2c^2 - 3c + 1 = 0 \) where \( c < 1 \)

### Tip:
When solving quadratic equations using the quadratic formula, always check the discriminant (\( b^2 - 4ac \)) to ensure the equation has real solutions. If the discriminant is positive, the equation has two real solutions; if it's zero, there is one real solution.

Would you like more details on any step or help with solving these similar exercises?

If a < 1. and 2a^2 - 7a +3= 0, what is the value of a? could you please solve this equation and create similar exercises

This page explains how to solve the quadratic equation 2a^2 - 7a + 3, given the condition a < 1, using the quadratic formula. Detailed step-by-step guidance is provided, along with five similar practice exercises. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation