(b) (x² - 2x + 5) by (4x – 3)
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Answer:
|x²+4x+3| = x² + 4x +3 when
x² + 4x +3 >= 0
x(x+3) >=0
i.e when x <= -3 or when x >= 0.....(1)
So the equation becomes
x² + 4x +3 + 2x +5 = 0
Which gives
x = - 4 and x = - 2
But we can't take x = - 2 as it not satisfies equation 1
So x = -4
Now |x² + 4x + 3| = -(x² + 4x + 3)
When x² + 4x + 3 <0
i.e when
-3 < x < 0.......(2)
So the equation becomes
-(x² + 4x + 3) + 2x+5 = 0
-x² -2x +2 = 0
x = √3 - 1 and x = -(√3+1)
But only x = - (√3+1) satisfy equation 2 so there are two answers
x = - 4 and x= - (√3 +1)