Find a cubic polynomial with the sum, some of the product of its zeroes taken two at a time, and the product of its zeroes as 2, -7, -14 respectively.
Ex 2.4 Class 10 Maths Question 3.
If the zeroes of the polynomial x3 – 3x2 + x + 1 are a-b, a, a + b, find a and b.
Solution:
Ex 2.4 Class 10 Maths Question 4.
If two zeroes of the polynomial x4 – 6x3 – 26x2 + 138x – 35 are 2 ± √3, find other zeroes.
Solution:
Ex 2.4 Class 10 Maths Question 5.
If the polynomial x4 – 6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 – 2x + k, the remainder comes out to be x + a, find k and a.
Solution:
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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