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4-2.Quadratic Equations and Inequations
hard
સમીકરણ $x|x|-5|x+2|+6$ = 0ના વાસ્તવિક બીજોની સંખ્યા $..........$ છે.
A
$5$
B
$3$
C
$6$
D
$4$
(JEE MAIN-2023)
Solution
$x|x|-5|x+2|+6=0$
$C-1:-x \in[0, \infty]$
$x^2-5 x-4=0$
$x=\frac{5 \pm \sqrt{25+16}}{2}=\frac{5+\sqrt{41}}{2}$
$x=\frac{5 \pm \sqrt{41}}{2}$
$C-2:-:-x \in[-2,0)$
$-x^2-5 x-4=0$
$x^2+5 x+4=0$
$x=-1,-4$
$x=-1$
$C-3: x \in[-\infty,-2)$
$-x^2+5 x+16=0$
$x^2-5 x-16=0$
$x=\frac{5 \pm \sqrt{25+64}}{2}$
$\frac{5 \pm \sqrt{89}}{2}$
$x=\frac{5-\sqrt{89}}{2}$
Standard 11
Mathematics
