PEAZIT Aha card
Go straight to resources ↓Quadratic equations: roots from the discriminant
For ax² + bx + c = 0, identify a, b, c including their signs. D = b² − 4ac determines the number of real roots.
| Expression | Meaning |
|---|---|
| a = 1; b = −5; c = 6 | The right side is already zero. |
| D = (−5)² − 4 · 1 · 6 = 1 | D is positive: two distinct real roots. |
| x = (5 ± √1)/2; x = 2; x = 3 | Use x = (−b ± √D)/(2a). |
One worked example
- a = 1; b = −5; c = 6The right side is already zero.
- D = (−5)² − 4 · 1 · 6 = 1D is positive: two distinct real roots.
- x = (5 ± √1)/2; x = 2; x = 3Use x = (−b ± √D)/(2a).
Watch out: D = 0 gives one repeated root; D < 0 gives no real roots. If a = 0, the equation is not quadratic.
Goal, prerequisites and card origin
What you will learn: Use the quadratic formula when a is nonzero.
What you need first: Powers, square roots and substitution with signs.
An original PEAZIT working card. Independent expert review and effectiveness testing have not yet taken place. · v1
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For ax² + bx + c = 0, identify a, b, c including their signs. D = b² − 4ac determines the number of real roots.