Exercise 2.3: Division Algorithm for Polynomials
You'll divide polynomials the long way — like long division with numbers, but with x's. Given some zeroes, you'll use division to find the rest.
Extra Practice Questions
These questions cover the same concepts as Exercise 2.3. Try solving them to build confidence before or after the textbook exercise.
If the square of the difference of the zeros of the quadratic polynomial f(x) = x² + px + 45 is 144, then the value of p is:
If the zeros of the quadratic polynomial `ax² + bx + c`, a ≠ 0, are equal in magnitude but opposite in sign, then which of the following is true?
A student claimed that if α and β are the zeros of the quadratic polynomial ax² + bx + c, then (α + β)² is always equal to (b/a)². Identify the mistake in the student's reasoning.
Ravi divided the polynomial `P(x) = x³ + 4x² + 5x - 2` by `G(x) = x + 2` and stated that the remainder is 4. Identify the mistake in Ravi's calculation.
The area of a rectangular plot is 528 m². The length of the plot (in meters) is one more than twice its breadth. Find the breadth of the plot.
If α and β are the zeros of the polynomial f(x) = x² - 10x + 24, then find the quadratic polynomial whose zeros are (α+β) and (2αβ).
If α and β are the zeros of the polynomial P(x) = 2x² - 3x + 5, form a quadratic polynomial whose zeros are 1/α and 1/β.
What should be added to the polynomial x³ + 2x² - 3x + 1 so that the resulting polynomial is exactly divisible by (x - 2)?
Which of the following quadratic polynomials has the sum of its zeros as -3 and the product of its zeros as 2?
If α and β are the zeros of the polynomial f(x) = x² + px + q, then find the value of (α/β + β/α).
Stuck on a question?
Paste any question from Exercise 2.3 into our AI Maths Solver and get a step-by-step solution instantly. It works for all NCERT questions.
Try AI Solver — FreeCommon Mistakes to Avoid
- ✗Errors in polynomial long division — write each step carefully
- ✗Forgetting to include zero-coefficient terms (e.g., 0x² when a power is missing)
- ✗Not checking the degree of remainder is less than the divisor
Other Exercises in Chapter 2
Frequently Asked Questions
How many questions are in Exercise 2.3?
Exercise 2.3 has 5 questions on polynomial long division and finding remaining zeroes given one or two zeroes.
What is the division algorithm for polynomials?
If p(x) and g(x) are polynomials with g(x) ≠ 0, then p(x) = g(x) × q(x) + r(x), where degree of r(x) < degree of g(x).
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