સમીકરણ |x{|^2} - 3|x| + 2 = 0 ના વાસ્તવિક બીજની સંખ?

English

Gujarati

Hindi

4-2.Quadratic Equations and Inequations

medium

સમીકરણ $|x{|^2}$-$3|x| + 2 = 0$ ના વાસ્તવિક બીજની સંખ્યા મેળવો.

$1$

$2$

$3$

$4$

(AIEEE-2003) (IIT-1982) (IIT-1989)

(d) Given $|x{|^2} – 3|x| + 2 = 0$

Here we consider two cases $viz.\,\,x < 0$and $x > 0$

Case I : $x < 0$ This gives ${x^2} + 3x + 2 = 0$

==> $(x + 2)(x + 1) = 0\,\, \Rightarrow x = – 2, – 1$

Also $x = – 1, – 2$satisfy $x < 0,$so $x = – 1$, $-2$ is solution in this case.

Case II : $x > 0$. This gives ${x^2} – 3x + 2 = 0$

==> $(x – 2)(x – 1) = 0\,\, \Rightarrow x = 2,1$, so $x = 2$,$ 1$ is solution in this case.

Hence the number of solutions are four i.e. $x = – 1,\,1,\,2,\, – 2$

Aliter : $|x{|^2} – 3|x| + 2 = 0$

==> $(|x| – 1)(|x| – 2) = 0$

==> $|x| = 1$and $|x| = 2$==> $x = \pm 1,x = \pm 2$.

Standard 11

Mathematics

hard

(JEE MAIN-2014)

normal

hard

(JEE MAIN-2014)

hard

(IIT-1980)

normal