For what values of k will the expression kx2+(k-2)x-(k+1) have no x term when simplified?

To find the value of \( k \) for which the expression \( kx^2 + (k-2)x - (k+1) \) has no \( x \) term when simplified, we need to make the coefficient of \( x \) equal to zero.

The given expression is:

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

For there to be no \( x \) term, the coefficient of \( x \), which is \( (k-2) \), must be equal to zero:

\[
k - 2 = 0
\]

Solving for \( k \):

\[
k = 2
\]

So, when \( k = 2 \), the expression will have no \( x \) term.

Let's verify by substituting \( k = 2 \) back into the expression:

\[
2x^2 + (2-2)x - (2+1) = 2x^2 + 0x - 3
\]

As we see, the \( x \) term vanishes, leaving the expression as \( 2x^2 - 3 \).

Thus, the expression will have no \( x \) term when \( k = 2 \).

Would you like more details or have any questions?

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Here are 5 related questions to deepen your understanding:

1. How does changing the value of \( k \) affect the overall quadratic expression?
2. What happens to the expression if \( k \) is negative?
3. Can there be multiple values of \( k \) that result in no \( x \) term?
4. What are the implications of having a zero coefficient for \( x^2 \) instead of \( x \)?
5. How would the expression change if the coefficient of \( x^2 \) were \( k+1 \) instead of \( k \)?

**Tip:** In quadratic expressions, the coefficient of each term plays a crucial role in determining the shape and position of the parabola represented by the equation.

For what values of k will the expression kx^2 + (k-2)x - (k+1) have no x term when simplified?

Explore how to find the value of k for which the quadratic expression kx^2 + (k-2)x - (k+1) simplifies with no x term. This problem involves core algebraic concepts and is ideal for students in Grades 8-10.

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