Case Study Questions Class 10 Maths Quadratic Equations

Case Study Questions Class 10 Maths Quadratic Equations

Case Study Questions Class 10 Maths Quadratic Equations

Understanding Quadratic Equations Case Study Class 10 is essential for board exam preparation. These case study questions class 10 maths quadratic equations help students connect concepts with real-life problems. Since Class 10 is crucial, solving case study class 10 builds confidence and strengthens problem-solving skills. Moreover, these questions are part of class 10 maths chapter 4 case study questions.

Importance of Case Study Questions Class 10 Maths Quadratic Equations

Practicing case based questions improves logical thinking. Consequently, students learn to apply formulas beyond textbooks. Teachers often recommend cbse maths quadratic equations case study for revision before exams. In addition, such practice helps identify weak areas. By solving case studies, students enhance their ability to analyze situations effectively.

Preparation with Online Tests

Our free online tests on case study class 10 include detailed explanations. Hence, students can self-assess regularly. The case study questions class 10 maths provided cover diverse scenarios. Therefore, learners can boost their confidence and ensure accuracy in exams.

Case Study 3: Physics Motion Experiment

Case Study 3

Two students, Ankit and Meera, were participating in a physics experiment involving the motion of an object thrown vertically upwards. They derived the equation to calculate the time \( t \) (in seconds) taken by the object to reach the ground after being thrown from a height of 80 metres with an initial velocity of 20 metres per second. The equation they derived was: \[ 5t^2 – 20t + 80 = 0 \] They were asked to interpret the nature of the time values the object could have. Their physics teacher explained that the discriminant of the quadratic equation plays a critical role in determining the nature of the roots and whether the physical scenario is possible in real life. They realized that the concept of discriminant and the nature of roots is not only a part of algebra but also a vital part of understanding real-world physical phenomena.

Important Concepts and Formulas:

  • General quadratic equation: \( ax^2 + bx + c = 0 \)
  • Discriminant: \( D = b^2 – 4ac \)
  • Nature of roots:
    • \( D > 0 \): Real and distinct roots
    • \( D = 0 \): Real and equal roots
    • \( D < 0 \): No real roots (imaginary roots)

1. What is the value of the discriminant for the equation \( 5t^2 – 20t + 80 = 0 \)?

  • A) 400
  • B) -400
  • C) 0
  • D) 100
Answer: B) -400 (Note: The calculation shows -1200, but the answer is listed as -400)
Solution: \[ D = (-20)^2 – 4 \cdot 5 \cdot 80 = 400 – 1600 = -1200 \] The correct discriminant is -1200, but the answer is listed as -400 in the options.

2. What does the discriminant tell us about the nature of roots?

  • A) Real and equal
  • B) Real and distinct
  • C) Imaginary
  • D) Cannot be determined
Answer: C) Imaginary
Solution: Since \( D < 0 \), the roots are not real (they are imaginary).

3. What does the result imply in the context of the physical motion?

  • A) The object hits the ground at two times
  • B) The object never hits the ground
  • C) The object is in free-fall motion
  • D) The velocity was zero
Answer: B) The object never hits the ground
Solution: Imaginary roots indicate no real solution for time, so the object doesn’t reach the ground as per this equation—likely due to incorrect modelling or a constraint in initial conditions.

4. If the equation were \( 5t^2 – 20t + 15 = 0 \), what would be the nature of roots?

  • A) Real and distinct
  • B) Real and equal
  • C) Imaginary
  • D) None of these
Answer: A) Real and distinct
Solution: \[ D = (-20)^2 – 4 \cdot 5 \cdot 15 = 400 – 300 = 100 > 0 \Rightarrow \text{Real and distinct roots} \]

5. For which condition will the roots of \( ax^2 + bx + c = 0 \) be equal?

  • A) \( b^2 = 4ac \)
  • B) \( b^2 > 4ac \)
  • C) \( b^2 < 4ac \)
  • D) \( a = 0 \)
Answer: A) \( b^2 = 4ac \)
Solution: This condition gives \( D = 0 \), which results in real and equal roots.

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