Using Vieta's Formulas | Math Competitions

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[@SidneiMV]

incredibly simple
x² - 5x + k = 0
4a - b = 10 => b = 4a - 10
a + b = a + 4a - 10 = 5 => a = 3
a = 3 => b = 2
ab = k => *k = 6*

[@phill3986]

👍👍👍😊😊😊

[@Skank_and_Gutterboy]

For method #1, if you switch x1 and x2, attempting to solve for k yields no solution. Why? Because after simplification, you wind up with:
sqrt(25-4k) = -1. No k will satisfy that equation. If 25-4k is positive, the square root will yield a positive number. If 25-4k is negative, the square root will yield a complex number. If 25-4k = 0, 0 cannot equal -1. There is no k that makes that equation work out, so x1 and x2 cannot be switched and k=6 is your only k-value.