https://r2.erweima.ai/mathbot/image/17260876626991utgo7gq.jpg

The equation in the image is a quadratic equation of the form:

\[
2x^2 - (k-1)x + (k+1) = 0
\]

In a general quadratic equation of the form \( ax^2 + bx + c = 0 \), the coefficients are:

- \( a = 2 \)
- \( b = -(k-1) = -k + 1 \)
- \( c = (k+1) \)

This equation could be solved for \( x \) using the quadratic formula:

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

Plugging in the values of \( a \), \( b \), and \( c \):

\[
x = \frac{-(-k+1) \pm \sqrt{(-k+1)^2 - 4(2)(k+1)}}{2(2)}
\]

Would you like me to continue solving this step-by-step, or do you have any specific questions? 

Here are some related questions for further exploration:
1. What is the discriminant, and how does it determine the nature of the roots?
2. Can this quadratic equation have real roots for all values of \( k \)?
3. How does changing \( k \) affect the solutions?
4. What is the graphical interpretation of this quadratic equation?
5. How does the quadratic formula relate to completing the square?

**Tip**: Always simplify the expression inside the square root (the discriminant) before moving on with the quadratic formula.

Solve the quadratic equation 2x^2 - (k-1)x + (k+1) = 0

Explore how to solve the quadratic equation 2x^2 - (k-1)x + (k+1) = 0, using algebraic concepts such as the quadratic formula. This step-by-step guide covers key concepts and calculations for students in Grades 9-11.

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