Exercise 2.3 Class X Math Chapter 2
Q. Find a quadratic polynomial whose sum and product of zeros are 1 and −6 respectively.
Solution:
Let zeros = α, β
Sum = α + β = 1
Product = αβ = −6
Required polynomial:x2−(α+β)x+αβ=x2−x−6
Answer: x2−x−6
অসমীয়া:
আৱশ্যক বহুপদী = x² − x − 6
🟢 5. Graphical Representation of Polynomial
English:
The number of zeros of a polynomial = number of points where the graph cuts the x-axis.
Assamese:
বহুপদীৰ গ্ৰাফে x-অক্ষ কিমানবাৰ কাটে = শূন্যৰ সংখ্যা।
🟢 6. Factor Theorem
English:
If p(a) = 0, then (x − a) is a factor of p(x).
Assamese:
যদি p(a) = 0 হয়, তেন্তে (x − a) বহুপদীৰ গুণনীয়ক।
🟢 Example (Factor Theorem)
Q. Find a factor of p(x) = x³ − 4x² − x + 4
Solution:
p(1) = 1 − 4 − 1 + 4 = 0
👉 (x − 1) is a factor.
অসমীয়া:
(x − 1) এটা গুণনীয়ক।
📌 HSLC Exam Tips (Very Important)
✔ Write formulas clearly
✔ Relationship questions = sure full marks
✔ Graph questions → neat diagram
✔ Use proper factorisation steps