Chapter 2 · Class 10 CBSE · Formula Sheet
Polynomials Formulas — Class 10 CBSE
Relate zeroes and coefficients of polynomials; perform division algorithm for polynomials.
Key Formulas
Linear (one zero)
\alpha = -\dfrac{b}{a}
Quadratic (sum of zeroes)
\alpha + \beta = -\dfrac{b}{a}
Quadratic (product of zeroes)
\alpha \beta = \dfrac{c}{a}
Cubic (sum)
\alpha + \beta + \gamma = -\dfrac{b}{a}
Cubic (sum of products)
\alpha\beta + \beta\gamma + \gamma\alpha = \dfrac{c}{a}
Cubic (product)
\alpha\beta\gamma = -\dfrac{d}{a}
Division Algorithm
p(x) = g(x) \cdot q(x) + r(x)
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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