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

Did you know that quadratic equations, like \( 2 k^{2} - 5 k + 3 \), have a long history dating back to ancient civilizations? The Babylonians were already solving equations similar to this over 4,000 years ago! Their methods laid the groundwork for algebra as we know it today, and they relied heavily on geometric interpretations. One common mistake when working with quadratics is neglecting to factor correctly or not checking the discriminant (the part under the square root in the quadratic formula). Always make sure to double-check your factoring and remember that if the discriminant is negative, your solutions will be complex numbers, which is perfectly normal but often overlooked by beginners!