Aspire's Library
A Place for Latest Exam wise Questions, Videos, Previous Year Papers,
Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
Consider the equation $x^{2}+4x-n=0$, where $n\in[20,100]$ is a natural number. Then the number of all distinct values of $n$, for which the given equation has integral roots, is equal to
Solution
$ x^2 + 4x - n = 0 $
Integral roots ⇒ discriminant perfect square
$ D = 16 + 4n = 4(4+n) $
$ 4+n = k^2 $
$ n = k^2 - 4 $
$ 20 \le n \le 100 $
$ 20 \le k^2 - 4 \le 100 $
$ 24 \le k^2 \le 104 $
Possible $ k^2 = 25, 36, 49, 64, 81, 100 $
So $ n = 21, 32, 45, 60, 77, 96 $
Total values $ = 6 $
$ \boxed{6} $
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Online Test Series, Information About Examination,
Syllabus, Notification
and More.
View More
Ask Your Question or Put Your Review.
