Polynomial Case Study Questions Class 10

Polynomial Case Study Questions Class 10

Polynomial Case Study Questions Class 10 | Free Online Test

Polynomial Case Study Questions Class 10

Students preparing for exams often search for case study math questions for class 10. These exercises help strengthen concepts in polynomials and their applications. Our online practice sets include interactive polynomial case study questions class 10 that focus on real-life problem solving. Practicing these questions regularly improves accuracy and speed. Additionally, students develop problem-solving skills while applying formulas like factorization and the remainder theorem in practical situations.

Importance of Polynomial Case Study Questions Class 10

Math case study questions class 10 on polynomials encourage analytical thinking and logical reasoning. For instance, questions based on finding zeros of polynomials or applying algebraic identities provide deeper understanding. Furthermore, solving these problems enhances critical thinking. Short exercises help reinforce key formulas and theorems. Therefore, students gain confidence and clarity in class 10 polynomials case study questions through consistent practice.

Benefits of Online Test Practice

Our polynomials case study class 10 online tests provide instant feedback and performance tracking. Students can quickly identify mistakes and improve their approach. The class 10 maths case study questions on polynomials cover multiple difficulty levels, from basic factorization to application-based sums. Consequently, learners strengthen concepts efficiently and are better prepared for board exams. Regular practice ensures mastery of fundamental polynomial concepts and boosts exam performance.

Case Study 2: Relationship Between Zeros and Coefficients

Case Study 2: Relationship Between Zeros and Coefficients

Ankita, a high school student preparing for her board exams, is revising quadratic polynomials. Her teacher explains that if \( \alpha \) and \( \beta \) are the zeros of a quadratic polynomial \( ax^2 + bx + c \), then these zeros have a specific relationship with the coefficients. She learns the following key formulas:

  • Sum of the zeros \( \alpha + \beta = -\dfrac{b}{a} \)
  • Product of the zeros \( \alpha \cdot \beta = \dfrac{c}{a} \)

Using these relationships, Ankita is able to form a quadratic polynomial when the zeros are known, using the formula:

\[ f(x) = x^2 – (\text{sum of zeros})x + (\text{product of zeros}) \]

With this knowledge, she works on the following problems:

1. If the zeros of the polynomial \( x^2 – 7x + 10 \) are \( \alpha \) and \( \beta \), what is \( \alpha + \beta \) and \( \alpha \cdot \beta \)?

  • A) \( 7, 10 \)
  • B) \( -7, 10 \)
  • C) \( 7, -10 \)
  • D) \( -7, -10 \)
Answer: A) \( 7, 10 \)
Solution: \[ \alpha + \beta = -\dfrac{-7}{1} = 7, \quad \alpha \cdot \beta = \dfrac{10}{1} = 10 \] Hence, the correct answer is option (a).

2. Find the quadratic polynomial whose zeros are 3 and 4.

  • A) \( x^2 – 7x + 12 \)
  • B) \( x^2 – 12x + 7 \)
  • C) \( x^2 + 7x + 12 \)
  • D) \( x^2 + 12x – 7 \)
Answer: A) \( x^2 – 7x + 12 \)
Solution: Sum = \( 3 + 4 = 7 \), Product = \( 3 \cdot 4 = 12 \) So the polynomial is: \[ x^2 – 7x + 12 \] Option (a) matches correctly.

3. If the sum and product of the zeros of a quadratic polynomial are 5 and 6 respectively, what is the polynomial?

  • A) \( x^2 – 5x + 6 \)
  • B) \( x^2 + 5x + 6 \)
  • C) \( x^2 – 6x + 5 \)
  • D) \( x^2 + 6x + 5 \)
Answer: A) \( x^2 – 5x + 6 \)
Solution: \[ f(x) = x^2 – (\text{sum})x + \text{product} = x^2 – 5x + 6 \] Option (a) is correct.

4. For the polynomial \( 2x^2 – 4x + 3 \), what is the sum and product of its zeros?

  • A) \( 2, 3 \)
  • B) \( 2, \dfrac{3}{2} \)
  • C) \( 2, \dfrac{3}{4} \)
  • D) \( \dfrac{4}{2}, \dfrac{3}{2} \)
Answer: B) \( 2, \dfrac{3}{2} \)
Solution: \[ \text{Sum of zeros} = -\dfrac{-4}{2} = 2, \quad \text{Product of zeros} = \dfrac{3}{2} \] Option (b) is correct.

5. What is the quadratic polynomial whose sum and product of zeros are both equal to 1?

  • A) \( x^2 – x + 1 \)
  • B) \( x^2 + x + 1 \)
  • C) \( x^2 – 1x + 1 \)
  • D) \( x^2 – 2x + 1 \)
Answer: C) \( x^2 – 1x + 1 \)
Solution: \[ f(x) = x^2 – (1)x + 1 = x^2 – x + 1 \] Both options (a) and (c) are equivalent. However, (c) writes the coefficient explicitly as \( -1x \), which aligns better with clarity. So, both are correct representations, but we will consider (c) based on form.

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