Topic 14 of 15, EHL Maths & Excel final (AP)
x²
Quadratic equations
A quadratic equation ax² + bx + c = 0 can have two, one or no real solutions. The delta (b² - 4ac) tells you which case you are in.
When the exam asks for it
- “solve”, “break-even with a squared term”, “x²”
Formulas
Delta
=B^2-4*A*CSolution 1
=(-B+SQRT(B^2-4*A*C))/(2*A)Solution 2
=(-B-SQRT(B^2-4*A*C))/(2*A)Worked example
D3fx
| A | B | C | D | E | |
|---|---|---|---|---|---|
| 1 | Case | A | B | C | |
| 2 | Equation x² - 5x + 6 = 0 | 1 | -5 | 6 | |
| 3 |
Sheet1
⬇ Download practice ExcelExample, Practice and Answers sheets with working formulas. Free.
Step by step
- Delta = (-5)^2 - 4*1*625 - 24 = 1 > 0 → two solutions
- x1 = (5 + 1)/23
- x2 = (5 - 1)/22
⚠ Exam traps
- delta > 0: two real solutions; delta = 0: one; delta < 0: none, and Excel shows #NUM! (square root of a negative number).
- Use brackets: 2*A in the denominator, not /2*A.
- B is negative here, so -B is +5. Refer to the cell, do not retype the sign.
Practice question
Solve x² - 6x + 9 = 0.
Show answer
✓ Delta = 36 - 36 = 0, so one solution: x = 6/2 = 3.
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