Question

Write the sum of real roots of the equation x² + |x| – 6 = 0.

Answer 1

Answer:

The sum of real roots of given quadratic equation is 0 .

Step-by-step explanation:

Given as :

The quadratic equation

$x^{2}+\left | x \right |-6 = 0$

Here The equation is in form of mode

So, two condition raise

( i ) for x positive

i.e  x $>$ 0

The equation can be written

x² + x - 6 = 0

x² + 3 x - 2 x- 6 = 0

Or, x ( x + 3) - 2 ( x + 3 ) = 0

i.e ( x + 3 ) ( x - 2 ) = 0

∴   x + 3 = 0           x - 2 = 0

i.e   x = - 3              x = 2

Therefor for   x $>$ 0   , we only consider value of x = 2

Again

( i ) for x negative

i.e  x $<$ 0

The equation can be written

x² - x - 6 = 0

x² - 3 x + 2 x - 6 = 0

Or, x ( x - 3) + 2 ( x - 3 ) = 0

i.e ( x - 3 ) ( x + 2 ) = 0

∴   x - 3 = 0           x + 2 = 0

i.e   x =  3              x = - 2

Therefor for   x $<$ 0  , we only consider value of x = - 2

Now, The sum of real roots = 2 + ( - 2 )

i.e  The sum of real roots = 2 - 2 = 0

Hence, The sum of real roots of given quadratic equation is 0 . Answer