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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.┬аFind whether the following equations have real roots. If real roots exist, find them
Solution:
Concept used: For a quadratic equation of the form,┬аax2┬а+┬аbx┬а+┬аc┬а= 0 to have real roots, its discriminant,┬аD┬а=┬аb2┬атАУ 4ac┬а> 0.
Question2.┬аFind 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┬аx.
According to the question,
┬а┬а┬а┬а┬а┬а┬а┬а┬а┬а x2┬атАУ 84 = 3 (x┬а+ 8)
тЯ╣┬а┬а┬а┬а┬а┬а┬аx2┬атАУ 84 = 3x┬а+ 24
тЯ╣┬а┬а┬а┬а┬а┬а┬аx2┬атАУ 3x┬атАУ 108 = 0
тЯ╣┬а┬а┬а┬а┬а┬а┬аx2┬атАУ 12x┬а+ 9x┬атАУ 108 = 0┬а [By splitting the middle trem]
тЯ╣┬а┬а┬а┬а┬а┬а┬аx┬а(x┬атАУ 12) + 9 (x┬атАУ 12) = 0
тЯ╣┬а┬а┬а┬а┬а┬а (x┬атАУ 12) (x┬а+ 9) = 0
тЯ╣┬а┬а┬а┬а┬а┬а┬аx┬а= 12, тАТ 9
Reject┬аx┬а= тАТ 9 value as a natural number canтАЩt be negative.
Hence, the required natural number is 12.
Question3.┬аA natural number, when increased by 12, equals 160 times its reciprocal. Find the number.
Solution:
Let the natural number be┬аx.
Reject┬аx┬а= тАУ 20 value as a natural number canтАЩt be negative.
Hence, the required natural number is 8.