Polynomials — Degree, Zeroes & the Magic Relations
What degree means, what 'zeroes' are, and the sum/product-of-zeroes shortcuts for quadratics.
By the PadhoDost Team · 📖 6 min read · Updated 4 August 2026
Part of Class 10 (CBSE) prepA polynomial is an expression like 3x² + 2x + 1 — terms with whole-number powers of x added together. The DEGREE is the highest power present.
| Degree | Name | Example |
|---|---|---|
| 1 | Linear | 2x + 3 |
| 2 | Quadratic | x² − 5x + 6 |
| 3 | Cubic | x³ + 1 |
What is a 'zero'?
🧠 Where it touches the ground
A zero of a polynomial is a value of x that makes it equal to 0 — graphically, where the curve crosses the x-axis. For x² − 4, the zeroes are x = 2 and x = −2 (since 2² − 4 = 0).
The magic relations (quadratics)
For a quadratic ax² + bx + c with zeroes α and β, you don't even need to solve it to know these:
📝 For x² − 5x + 6 (a = 1, b = −5, c = 6):
Sum of zeroes = −(−5)/1 = 5
Product of zeroes = 6/1 = 6
Check: zeroes are 2 and 3 → 2 + 3 = 5 ✓ and 2 × 3 = 6 ✓
⚡ Quick check
For ax² + bx + c, the product of the zeroes is:
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