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The sum of the roots of the equation, $x^{2}+\left | 2x-3 \right |-4=0$ ,is

Option 1)
$2$

Option 2)
$-2$

Option 3)
$\sqrt{2}$

Option 4)
$-\sqrt{2}$

Answers (2)

best_answer

As we have learned

Roots of Quadratic Equation -

$\alpha = \frac{-b+\sqrt{b^{2}-4ac}}{2a}$

$\beta = \frac{-b-\sqrt{b^{2}-4ac}}{2a}$

- wherein

$ax^{2}+bx+c= 0$

is the equation

$a,b,c\in R,\: \: a\neq 0$

Case (1) $x\geq 3/2$

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

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

$\Rightarrow x = \frac{-2 \pm \sqrt{4+28}}{2}= -1\pm 2\sqrt2$

Acceptable value = $2 \sqrt 2-1$

case (2)

x < 3/2

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

$x^2-2x-1= 0$

$\Rightarrow x= \frac{2\pm \sqrt{4+4}}{2}= 1\pm \sqrt2$

Acceptable value $1-\sqrt2$

sum of roots = $1-\sqrt2+ 2\sqrt2-1 = \sqrt 2$

Option 1)

$2$

Option 2)

$-2$

Option 3)

$\sqrt{2}$

Option 4)

$-\sqrt{2}$

Posted by

Himanshu

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