Solving Quadratics Four Ways
Key methods, formulas, and traps for solving quadratic equations on the PSAT.
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Questions Covered in This Set
10 cards to master
Standard form of a quadratic equation
ax² + bx + c = 0, with a ≠ 0
Zero-product property
If AB = 0, then A = 0 or B = 0 — set each factor equal to zero after factoring.
When should you use the square-root method?
When there's no lone x term (or the equation is already a squared binomial). Isolate the square and take ± the square root.
Most common careless error with square roots
Forgetting the negative root — always write ±.
Why can't you divide both sides of 2x² = 10x by x?
You'd lose the solution x = 0. Factor instead: 2x(x − 5) = 0 → x = 0 or 5.
Steps to complete the square for x² + bx = c
Add (b/2)² to both sides, factor the left as (x + b/2)², then take ± the square root.
The quadratic formula
x = (−b ± √(b² − 4ac)) / (2a)
Discriminant and number of real solutions
b² − 4ac > 0 → two real; = 0 → exactly one (repeated); < 0 → none.
Sum and product of the solutions
Sum = −b/a, product = c/a.
For what positive k does x² + kx + 9 = 0 have exactly one solution?
Set k² − 4(1)(9) = 0 → k² = 36 → k = 6.
