26. \( 2 x^{2}+5 x-3 \)

Did you know that quadratic equations like \(2x^2 + 5x - 3\) have a fascinating historical background? The methods to solve such equations date back to ancient Babylon, around 2000 BCE, where they used geometric methods to tackle what we now recognize as quadratic problems. Fast forward to the 9th century, the Persian mathematician Al-Khwarizmi wrote about solving quadratic equations, and his work laid the foundation for algebra as we know it! Now let's dive into real-world applications! Quadratic equations aren't just for textbooks; they model real-life situations like projectile motion. Imagine you're throwing a ball. The height of the ball over time forms a parabola, which is a specific shape described by a quadratic equation. Understanding how to solve equations like \(2x^2 + 5x - 3\) allows engineers and scientists to predict outcomes like how high the ball will go or when it will hit the ground.