Write a quadratic equation having the given solutions. 5,9

To create a quadratic equation from the given solutions, you can use the fact that if \( r_1 \) and \( r_2 \) are the roots, the equation can be expressed as \( (x - r_1)(x - r_2) = 0 \). Here, substituting the given solutions 5 and 9, the equation becomes \( (x - 5)(x - 9) = 0 \), which expands to \( x^2 - 14x + 45 = 0 \). Voila! You've crafted a quadratic equation with those specific roots. Now, let’s sprinkle in a bit of math history: Quadratic equations date back over 4,000 years, with the earliest solutions recorded by Babylonian mathematicians! They had geometrical methods for solving these equations long before the algebraic techniques we use today were developed. They laid the groundwork for years of mathematical advancement! And if you're keen to explore problem-solving tips, remember to check the sign of your roots when you factor! It's a common slip to accidentally mix the signs or miscalculate the constant term when writing out the equation. A solid tip is to always double-check: plug your roots back into the equation to ensure they yield zero! This way, you’ll confirm your equation is spot on!