7
CBSE Marks
★★★★★
Difficulty
7
Topics
Medium
Board Weight
Topics Covered
7 key topics in this chapter
Geometrical Meaning of Zeros
Number of Zeros of a Polynomial
Relationship: Zeros & Coefficients (Quadratic)
Relationship: Zeros & Coefficients (Cubic)
Division Algorithm for Polynomials
Finding Zeros Given Sum/Product
Verifying Zeros of Polynomials
Study Resources
Key Formulas
| Formula / Rule | Expression |
|---|---|
| Sum of Zeros (Quadratic) | \(α + β = −b/a\) |
| Product of Zeros (Quadratic) | \(αβ = c/a\) |
| Sum of Zeros (Cubic) | \(α+β+γ = −b/a\) |
| Product of Zeros (Cubic) | \(αβγ = −d/a\) |
| Division Algorithm | \(p(x) = g(x)·q(x) + r(x)\) |
Important Points to Remember
The number of zeros of a polynomial p(x) equals the number of times the graph of y = p(x) cuts (or touches) the x-axis.
A quadratic polynomial can have at most 2 zeros; a cubic polynomial at most 3.
If α and β are zeros of ax²+bx+c: sum = −b/a, product = c/a.
If α, β, γ are zeros of ax³+bx²+cx+d: sum = −b/a, sum of products of pairs = c/a, product = −d/a.