In this article you will get CBSE Class 10 Mathematics chapter 4, Quadratic Equations: NCERT Exemplar Problems and Solutions (Part-IVA). Every question has been provided with a detailed solution. All the questions given in this article are very important to prepare for CBSE Class 10 Board Exam 2017-2018.
Find below the NCERT Exemplar problems and their solutions for Class 10 Mathematics Chapter, Quadratic Equations:
Exercise 4.4
Long Answer Type Questions
Question1. Find whether the following equations have real roots. If real roots exist, find them
Solution:
Concept used: For a quadratic equation of the form, ax2 + bx + c = 0 to have real roots, its discriminant, D = b2 – 4ac > 0.
Question2. Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.
Solution:
Let the required natural number be x.
According to the question,
x2 – 84 = 3 (x + 8)
⟹ x2 – 84 = 3x + 24
⟹ x2 – 3x – 108 = 0
⟹ x2 – 12x + 9x – 108 = 0 [By splitting the middle trem]
⟹ x (x – 12) + 9 (x – 12) = 0
⟹ (x – 12) (x + 9) = 0
⟹ x = 12, ‒ 9
Reject x = ‒ 9 value as a natural number can’t be negative.
Hence, the required natural number is 12.
Question3. A natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
Solution:
Let the natural number be x.
Reject x = – 20 value as a natural number can’t be negative.
Hence, the required natural number is 8.