Two roots, α and β, always balance against the coefficients of their equation. Learn the relationship once, then drill it until it's mental math — 100 questions, easiest first.
For x² + bx + c = 0
α + β = −b
The sum of the roots is the coefficient of x, sign flipped.
For x² + bx + c = 0
αβ = c
The product of the roots is just the constant term.
General form, ax² + bx + c = 0
α+β = −b/a · αβ = c/a
Same idea — divide by the leading coefficient first.
Worked example. For x² − 5x + 6 = 0: sum = −(−5) = 5, product = 6. Check: 2 and 3 add to 5 and multiply to 6. ✓ You never need to solve the equation to know its roots' sum and product.
Try it yourself — ax² + bx + c = 0
sum = 5 · product = 6
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Roots & Coefficients — Answer Key
Top Edu Prep · SAT Math · Algebra 2 / Precalculus · 100 questions