Sum and product of roots
Equations and inequalities · Mathematics
Study notes
Q: If α, β are roots of 2x² - 7x + 3 = 0, find α + β, αβ, and α² + β² without solving. Step 1: Sum = -b/a = 7/2. Step 2: Product = c/a = 3/2. Step 3: α² + β² = (α+β)² - 2αβ = (7/2)² - 2(3/2) = 49/4 - 3 = 37/4. Verify: roots are 3, 1/2. Sum = 7/2 ✓, product = 3/2 ✓.