Quadratic equations · द्विघात समीकरण
Type a, b, c — get D, the nature of roots and the roots with steps. Then practise.
Quadratic equations games
Quadratic equation solver · द्विघात समीकरण
ax² + bx + c = 0
Formulas
| Standard form | ax² + bx + c = 0, a ≠ 0 |
|---|---|
| Discriminant (विविक्तकर) | D = b² − 4ac |
| Quadratic formula (श्रीधराचार्य सूत्र) | x = (−b ± √D) / 2a |
| Nature of roots | D > 0: two distinct real · D = 0: two equal real · D < 0: no real roots |
| Roots α, β | α + β = −b/a, αβ = c/a |
Methods: factorisation (split the middle term), completing the square, the quadratic formula.
For Class 10 (NCERT Mathematics 10, “Quadratic Equations”). Practice answers are computed and checked by a program.
A one-page chart to stick on the wall, and a worksheet to practise.
Quadratic equations
ax² + bx + c = 0 · D = b² − 4ac · x = (−b ± √D)/2a · α+β = −b/a · αβ = c/a
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Quadratic equations — worksheet
Name: ____________________ Class: ______ Date: __________
1. Solve: x² − 5x + 6 = 0
2. Solve: 2x² + x − 6 = 0
3. Find the nature of roots: 3x² − 2x + 1 = 0
4. Find k if x² + kx + 9 = 0 has equal roots.
5. The product of two consecutive positive integers is 306. Find them.
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