Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and their coefficients:
(i) x2 – 2x – 8
(ii) 4s2 – 4s + 1
(iii) 6x2 – 3 – 7x
(iv) 4u2 + 8u
(v) t2 – 15
(vi) 3x2 – x – 4
CBSE Class 10 Polynomials — Complete Guide
Polynomials is a scoring chapter in CBSE Class 10 Mathematics, worth 3-4 marks. Master the zeros-coefficient relationship and division algorithm for guaranteed marks.
Quick Revision: Key Concepts
- Zeros: Values of x where p(x) = 0 (x-intercepts on graph)
- Sum of zeros (α + β): −b/a
- Product of zeros (αβ): c/a
- Form polynomial: k[x² − (sum)x + (product)]
- Division algorithm: p(x) = g(x) × q(x) + r(x)
Board Exam Pattern
1-2 MCQs on zeros-coefficient relationship, 1 short answer on finding zeros and verifying relationship or forming a polynomial from given zeros.
Most Important Questions
- Find zeros of a quadratic polynomial and verify sum/product relationship
- Find quadratic polynomial with given sum and product of zeros
- Divide one polynomial by another and verify division algorithm
- Find remaining zeros given one or two zeros
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