quadratic equation has solutions 2x ^ 2 + kx + k = 0

To find the solutions of the quadratic equation \( 2x^2 + kx + k = 0 \), we will use the **quadratic formula**:

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

In your equation, \( 2x^2 + kx + k = 0 \), the coefficients are:

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

Now, substitute these values into the quadratic formula:

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

Simplifying inside the square root:

\[
x = \frac{-k \pm \sqrt{k^2 - 8k}}{4}
\]

Thus, the solutions are:

\[
x = \frac{-k \pm \sqrt{k(k - 8)}}{4}
\]

So, the roots of the quadratic equation \( 2x^2 + kx + k = 0 \) are:

\[
x = \frac{-k \pm \sqrt{k(k - 8)}}{4}
\]

Would you like further clarification on any step?

Here are 5 related questions:

1. What are the conditions for real solutions in a quadratic equation?
2. How do we use the discriminant to determine the nature of the roots?
3. What happens when \( k = 0 \) in this quadratic equation?
4. How do we factor quadratic equations when possible?
5. How does the quadratic formula change when the leading coefficient is different from 1?

**Tip:** Always check the discriminant \( b^2 - 4ac \) to know whether a quadratic equation has real or complex solutions.

quadratic equation has solutions 2x^2 + kx + k = 0

Explore how to solve the quadratic equation 2x^2 + kx + k = 0 using the quadratic formula. This tutorial covers key algebra concepts, including finding the roots using discriminants. Suitable for students in Grades 9-12.

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