quadratic equations anamoly

[theamit]

Hello,

as i was making my way through quadratic equations,i stumbled upon these two types of problems i don't understand how to solve.


Find sum of the real roots of the equations -

1) x² + lxl - 6 = 0 ^(ans=0)


2)

(ans=4)

thanks.

 

[pka]

Find sum of the real roots of the equations -
1) x² + lxl - 6 = 0 ^(ans=0)
2)

(ans=4)

1) There are two cases:
\(\displaystyle x\ge 0\) AND \(\displaystyle x^2+x-6=0\)

\(\displaystyle x< 0\) AND \(\displaystyle x^2-x-6=0\).

Solve each and get \(\displaystyle x=\pm 2\).

2) Solve \(\displaystyle u=x-2\) AND \(\displaystyle u^2+u-2=0\)

 

[Steven G]

Hello,

as i was making my way through quadratic equations,i stumbled upon these two types of problems i don't understand how to solve.


Find sum of the real roots of the equations -

1) x² + lxl - 6 = 0 ^(ans=0)


2)

(ans=4)

thanks.

You need to use the definition of |x|. |x|= x, if x>= 0 and |x|= -x, if x<0.