**Case study Questions on the Class 10 Mathematics Chapter 4 **are very important to solve for your exam. Class 10 Maths Chapter 4 Case Study Questions have been prepared for the latest exam pattern. You can check your knowledge by solving case study-based** **questions for Class 10 Maths Chapter 4 **Quadratic Equations**

In CBSE Class 10 Maths Paper, Students will have to answer some questions based on Assertion and Reason. There will be a few questions based on case studies and passage-based as well. In that, a paragraph will be given, and then the MCQ questions based on it will be asked.

# Quadratic Equations Case Study Questions With answers

Here, we have provided case-based/passage-based questions for Class 10 Maths **Chapter 4 Quadratic Equations**

**Case Study/Passage Based Questions**

**1)Formation of Quadratic Equation**

Quadratic equations started around 3000 B.C. with the Babylonians. They were one of the world’s first civilizations and came up with some great ideas like agriculture, irrigation, and writing. There were many reasons why Babylonians needed to solve quadratic equations. For example to know what amount of crop you can grow on the square field.

Now represent the following situations in the form of a quadratic equation.

**The sum of squares of two consecutive integers is 650.**(a) x

^{2}+ 2x – 650 = 0 (b) 2x

^{2}+2x – 649 = 0

(c) x

^{2}– 2x – 650 = 0 (d) 2x

^{2}+ 6x – 550 = 0

Answer: (b) 2×2 +2x – 649 = 0

**The sum of two numbers is 15 and the sum of their reciprocals is 3/10.**(a) x

^{2}+ 10x – 150 = 0

(b) 15x

^{2}– x + 150 = 0

(c) x

^{2}– 15x + 50 = 0

(d) 3x

^{2}– 10x + 15 = 0

Answer: (c) x2 – 15x + 50 = 0

**Two numbers differ by 3 and their product is 504.**(a) 3x

^{2}– 504 = 0 (b) x

^{2}– 504x + 3 = 0

(c) 504x

^{2}+3 = x (d) x

^{2}+ 3x – 504 = 0

Answer: (d) x2 + 3x – 504 = 0

**A natural number whose square diminished by 84 is thrice of 8 more of a given number.**(a) x

^{2}+ 8x – 84 = 0 (b) 3x

^{2}– 84x + 3 = 0

(c) x

^{2}– 3x – 108 = 0 (d) x

^{2}–11x + 60 = 0

Answer: (c) x2 – 3x – 108 = 0

**A natural number when increased by 12, equals 160 times its reciprocal.**(a) x

^{2}– 12x + 160 = 0 (b) x

^{2}– 160x + 12 = 0

(c) 12x

^{2}– x – 160 = 0 (d) x

^{2}+ 12x – 160 = 0

Answer: (d) x2 + 12x – 160 = 0

**2)Nature of Roots**A quadratic equation can be defined as an equation of degree 2. This means that the highest exponent of the polynomial in it is 2. The standard form of a quadratic equation is ax

^{2}+ bx + c = 0, where a, b, and c are real numbers and a ≠ 0. Every quadratic equation has two roots depending on the nature of its discriminant, D = b

^{2}– 4ac

**Which of the following quadratic equation have no real roots?**(a) –4x

^{2}+ 7x – 4 = 0 (b) –4x

^{2}+ 7x – 2 = 0

(c) –2x

^{2}+5x – 2 = 0 (d) 3x

^{2}+ 6x + 2 = 0

Answer: (a) –4×2 + 7x – 4 = 0

**Which of the following quadratic equation have rational roots?**(a) x

^{2}+ x – 1 = 0

(b) x

^{2}– 5x + 6 = 0

(c) 4x

^{2}– 3x – 2 = 0

(d) 6x

^{2}– x + 11 = 0

Answer: (b) x2 – 5x + 6 = 0

**Which of the following quadratic equation have irrational roots?**(a) 3x

^{2}+2x + 2 = 0

(b) 4x

^{2}– 7x + 3 = 0

(c) 6x

^{2}– 3x – 5 = 0

(d) 2x

^{2}+3x – 2 = 0

Answer: (c) 6×2 – 3x – 5 = 0

**Which of the following quadratic equations have equal roots?**(a) x

^{2}– 3x + 4 = 0 (b) 2x

^{2}– 2x + 1 = 0

(c) 5x

^{2}– 10x + 1 = 0 (d) 9x

^{2}+ 6x + 1 = 0

Answer: (d) 9×2 + 6x + 1 = 0

**Which of the following quadratic equations has two distinct real roots?**(a) x

^{2}+ 3x + 1 = 0 (b) –x

^{2}+ 3x – 3 = 0

(c) 4x

^{2}+ 8x + 4 = 0 (d) 3x

^{2}+ 6x + 4 = 0

Answer: (a) x2 + 3x + 1 = 0

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