1) \( 2 x^{2}-7 x-4 \) 2) \( 3 x^{2}-8 x+4 \) 3) \( 3 x^{2}-6 x+4 \) 4) \( 2 x^{3}+4 x^{2}-6 x \) 5) \( 3 x^{2}+5 x-2 \)

Did you know that quadratic equations, like \(2x^2 - 7x - 4\) and the others on your list, were used by ancient civilizations as early as 2000 BC? The Babylonians had methods for solving them, but they didn’t use modern notation. Instead, they relied on geometric interpretations, which laid the groundwork for algebra as we know it today! When tackling these quadratic equations, a common mistake is neglecting the discriminant when finding roots. The discriminant \(D = b^2 - 4ac\) tells you about the nature of the roots. If \(D > 0\), you get two real roots; if \(D = 0\), there's one repeated real root; and if \(D < 0\), the roots are complex. So always check the discriminant before diving in!