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The problem asks to determine the value of \( X_1 \cdot X_2 \), where \( X_1 \) and \( X_2 \) are the roots of the quadratic equation:

\[
2x^2 + x - 10 = 0
\]

To solve this, we can use Vieta's formulas, which relate the coefficients of a quadratic equation to the sum and product of its roots. For a general quadratic equation \( ax^2 + bx + c = 0 \), the formulas are:

- Sum of the roots: \( X_1 + X_2 = -\frac{b}{a} \)
- Product of the roots: \( X_1 \cdot X_2 = \frac{c}{a} \)

Here, \( a = 2 \), \( b = 1 \), and \( c = -10 \). Using the formula for the product of the roots:

\[
X_1 \cdot X_2 = \frac{c}{a} = \frac{-10}{2} = -5
\]

Thus, the value of \( X_1 \cdot X_2 \) is \( -5 \).

Would you like further details or explanations?

Here are five related questions to explore further:

1. How do we calculate the sum of the roots \( X_1 + X_2 \)?
2. How can we solve this quadratic equation by factoring or using the quadratic formula?
3. What is Vieta’s theorem, and how does it apply to higher-degree polynomials?
4. How would the solution change if the equation were \( 2x^2 + x + 10 = 0 \)?
5. Can the quadratic equation \( 2x^2 + x - 10 = 0 \) have complex roots, and under what conditions?

**Tip:** Vieta's formulas are a powerful tool to quickly find relationships between the roots of polynomial equations without solving for the exact roots.

Jika X1 dan X2 adalah akar dari persamaan 2x^2 + x - 10 = 0, Tentukan nilai dari X1 * X2!

Solve the quadratic equation 2x^2 + x - 10 = 0 and find the product of its roots using Vieta's Formulas. This problem is suitable for students in Grades 9-11, covering key algebraic concepts and formulas.

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