The quadratic equation x2+kx+2k−3=0
 has equal roots.

The possible value(s) of k
 are

Given the quadratic equation \( x^2 + kx + 2k - 3 = 0 \), we are told that it has equal roots. For a quadratic equation to have equal roots, the discriminant (\( \Delta \)) must be equal to zero.

The general form of a quadratic equation is \( ax^2 + bx + c = 0 \), and the discriminant is given by:

\[
\Delta = b^2 - 4ac
\]

In this case, comparing \( x^2 + kx + (2k - 3) = 0 \) with the standard form, we have:
- \( a = 1 \)
- \( b = k \)
- \( c = 2k - 3 \)

Now, calculate the discriminant:

\[
\Delta = k^2 - 4(1)(2k - 3)
\]

Simplifying:

\[
\Delta = k^2 - 4(2k - 3) = k^2 - 8k + 12
\]

Since the equation has equal roots, set the discriminant equal to zero:

\[
k^2 - 8k + 12 = 0
\]

Solve this quadratic equation:

\[
k = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(1)(12)}}{2(1)}
\]

\[
k = \frac{8 \pm \sqrt{64 - 48}}{2}
\]

\[
k = \frac{8 \pm \sqrt{16}}{2}
\]

\[
k = \frac{8 \pm 4}{2}
\]

This gives two possible solutions for \( k \):

\[
k = \frac{8 + 4}{2} = 6 \quad \text{or} \quad k = \frac{8 - 4}{2} = 2
\]

Thus, the possible values of \( k \) are \( k = 6 \) and \( k = 2 \).

### Do you want further details or explanations on any step?

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Here are 5 related questions to further your understanding:
1. What is the meaning of the discriminant in a quadratic equation?
2. How would the solution change if the roots were not equal but real and distinct?
3. Can you derive the quadratic formula used to solve for \( k \)?
4. How does the sign of the discriminant affect the nature of the roots of a quadratic equation?
5. What are the conditions for a quadratic equation to have imaginary roots?

**Tip:** Always check if a quadratic equation is factorable before applying the quadratic formula—it might save you time!

The quadratic equation x^2 + kx + 2k - 3 = 0 has equal roots. The possible value(s) of k are

Discover how to solve the quadratic equation x^2 + kx + 2k - 3 = 0 with equal roots. Learn key concepts like the discriminant and the quadratic formula, and find the values of k that satisfy the equation. Ideal for students in Grades 9-11.

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