4.2 Quadratic equations and inequations — ગણિત ધોરણ 11 સાયન્સ — Question

$|2 x-3|=\left\{\begin{array}{ccc}{(2 x-3)} & {\text { if }} & {x>\frac{3}{2}} \\ {-(2 x-3)} & {\text { if }} & {x<\frac{3}{2}}\end{array}\right.$

for $x>\frac{3}{2},$

$x^{2}+2 x-3-4=0$

$x^{2}+2 x-7=0$

$x=\frac{-2 \pm \sqrt{4+28}}{2}$

$ = \frac{{ - 2 \pm 4\sqrt 2 }}{2} =  - 1 \pm 2\sqrt 2 $

Here $x=2 \sqrt{2}-1$

$\left\{2 \sqrt{2}-1<\frac{3}{2}\right\}$

for $x<\frac{3}{2}$

$x^{2}-2 x+3-4=0$

$\Rightarrow x^{2}-2 x-1=0$

$ \Rightarrow x = \frac{{2 \pm \sqrt {4 + 4} }}{2}$

$= \frac{{2 \pm 2\sqrt 2 }}{2}$

$= 1 \pm \sqrt 2 $

Here $x=1-\sqrt{2} \quad\left\{(1-\sqrt{2})<\frac{3}{2}\right\}$

Sum of roots : $(2 \sqrt{2}-1)+(1-\sqrt{2})=\sqrt{2}$