Chapter 4 · Class 10 CBSE · Formula Sheet
Quadratic Equations Formulas — Class 10 CBSE
Solve quadratic equations using factorization and quadratic formula; determine nature of roots.
Key Formulas
Standard Form
ax^2 + bx + c = 0, \quad a \neq 0
Quadratic Formula
x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}
Discriminant
D = b^2 - 4ac
Nature of Roots (D > 0)
\text{Two distinct real roots}
Nature of Roots (D = 0)
\text{Two equal real roots}
Nature of Roots (D < 0)
\text{No real roots}
Sum of Roots
\alpha + \beta = -\dfrac{b}{a}
Product of Roots
\alpha \cdot \beta = \dfrac{c}{a}
Worked Examples
1Using: Linear Equation
Solve 3x + 5 = 20.
Step 1: 3x = 20 - 5 = 15.
Step 2: x = 15 / 3 = 5.
Answer: x = 5
2Using: Algebraic Identity
Expand (a + 3)^2.
Step 1: Using (a + b)^2 = a^2 + 2ab + b^2
Step 2: = a^2 + 6a + 9.
Answer: a^2 + 6a + 9
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