Welcome to StudyMats. This comprehensive educational guide for Class 10 Maths – Chapter 2: Polynomials Important Questions is prepared to assist students in preparing effectively for their school, board, and competitive examinations. All questions, exercise solutions, and concept notes strictly adhere to the latest NCERT curriculum and CBSE guidelines.
Class 10 Maths – Chapter 2: Polynomials Important Questions
Q1. Which of the following is a polynomial?
निम्न में से कौन-सा बहुपद है?
(a) 1/x + 2 (b) x² + 2x + 1 (c) x⁻² + 3x (d) √x + 1
Q2. Find degree of 5x⁴ + 2x³ − x + 7
बहुपद 5x⁴ + 2x³ − x + 7 की घात ज्ञात कीजिए।
Q3. Find p(x) = x² − 4x + 4 at x = 2
p(x) = x² − 4x + 4 का मान x = 2 पर।
Q4. If one zero of x² + 7x + 12 is −3, find other zero
x² + 7x + 12 का एक शून्यक −3, दूसरा ज्ञात करें।
Q5. Find zeroes of x² − 2x − 8
x² − 2x − 8 के शून्यक ज्ञात कीजिए।
Q6. Check if −2 is zero of p(x) = x³ + x² − 2x
−2, p(x) = x³ + x² − 2x का शून्यक है?
Q7. Sum & product of zeroes of 2x² − 8x + 6
2x² − 8x + 6 के शून्यकों का योग-गुणनफल।
Q8. If α, β zeroes of x² + 7x + 10, find 1/α + 1/β
α, β शून्यक तो 1/α + 1/β ज्ञात करें।
Q9. Quadratic polynomial: sum of zeroes = 5, product = 6
शून्यक योग=5, गुणनफल=6 का द्विघात बहुपद।
Q10. One zero of (k−1)x² + kx + 1 is −3, find k
(k−1)x² + kx + 1 का शून्यक −3, k ज्ञात करें।
Q11. Zeroes of 4x² − 4x + 1 & verify relationship
4x² − 4x + 1 के शून्यक व संबंध सत्यापित करें।
Q12. If α, β zeroes of x² − 5x + 4, find α² + β²
x² − 5x + 4 के शून्यकों का α² + β²।
Q13. Divide 3x³ + x² + 2x + 5 by x² + 2x + 1
3x³ + x² + 2x + 5 को x² + 2x + 1 से भाग दें।
Q14. Quadratic polynomial with zeroes (2+√3), (2−√3)
शून्यक (2+√3), (2−√3) का द्विघात बहुपद।
Q15. If (x + a) factor of 2x² + 2ax + 5x + 10, find a
(x + a) गुणनखंड तो a ज्ञात करें।
Q16. All zeroes of x³ + 3x² − 2x − 6 (one zero = √2)
x³ + 3x² − 2x − 6 के सभी शून्यक (√2 दिया गया)।
Q17. Subtract from x³ − 6x² − 15x + 80 to make divisible by x² + x − 12
x³ − 6x² − 15x + 80 को x² + x − 12 से विभाज्य बनाने हेतु घटाना।
Q18. Verify Division Algorithm: p(x)=x⁴−5x+6, g(x)=2−x²
Division Algorithm सत्यापित करें।
Q19. α, β zeroes of kx² + 4x + 4, α² + β² = 24, find k
kx² + 4x + 4 के शून्यक, α² + β² = 24 तो k।
Q20. Polynomial graph cuts x-axis at 3 points. How many zeroes?
ग्राफ x-अक्ष को 3 बिंदुओं पर काटे तो शून्यक कितने?
💡 Important Exam & Study Tips
- Master NCERT Fundamentals: Ensure thorough familiarity with standard textbook definitions, formulas, and in-text examples before solving advanced problems.
- Step-by-Step Presentation: In board examinations, neat presentation, correct formula application, and labeled steps earn maximum step-marking.
- Practice Under Timed Conditions: Regular practice with previous years' question papers (PYQs) builds exam speed and accuracy.
📚 Related Study Materials on StudyMats
Access more chapter-wise notes and practice papers:
- StudyMats Home — Complete Educational Study Material
- Division Algorithm Study Notes & Question Papers
- Factor Theorem Study Notes & Question Papers
- Polynomials Study Notes & Question Papers
- Quadratic Polynomial Study Notes & Question Papers
❓ Frequently Asked Questions (FAQs)
Q1: Are these solutions aligned with the latest rationalized syllabus?
Yes, all study notes and practice questions on StudyMats strictly follow the updated NCERT textbook pattern and CBSE assessment guidelines.
Q2: How can I prepare this chapter for highest marks?
Review the theory thoroughly, solve all textbook exercise questions, and repeatedly practice the high-frequency questions provided in this guide.