Formation of equations from roots
Equations and inequalities · Mathematics
Study notes
Q: Form a quadratic with roots 5 and -3. Form one with roots 1/2 and 1/3. Part A: Sum = 5 + (-3) = 2. Product = 5 × (-3) = -15. Equation: x² - 2x - 15 = 0. Part B: Sum = 1/2 + 1/3 = 5/6. Product = 1/6. Equation: x² - (5/6)x + 1/6 = 0. Multiply by 6: 6x² - 5x + 1 = 0. Check A: x = 5: 25 - 10 - 15 = 0 ✓.