find the value of a so that x+6 is a factor of x³+ 3x²+4x+a
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We have |x| < a
We know that |x| = (x if x ≥ 0 ) and (-x if x < 0)
So, we consider the following cases :
CASE I :- When x ≥ 0
In this case |x| = x -----------> Therefore x < a
Thus in this case the solution set of the given Inequation is given by
X ≥ 0 and x < a -----------> 0 ≤ x < a
CASE II :- When x < 0
In this case |x| = - x -----------> Therefore - x < a --------> x > -a
Thus in this case the solution set of the given Inequation is given by
X < 0 and x > - a -----------> -a < x < 0
Combining two cases together, we get (-a < x < 0) or ( 0 ≤ x < a)
Once we take extreme points, we get –a < x < a
We know that |x| = (x if x ≥ 0 ) and (-x if x < 0)
So, we consider the following cases :
CASE I :- When x ≥ 0
In this case |x| = x -----------> Therefore x < a
Thus in this case the solution set of the given Inequation is given by
X ≥ 0 and x < a -----------> 0 ≤ x < a
CASE II :- When x < 0
In this case |x| = - x -----------> Therefore - x < a --------> x > -a
Thus in this case the solution set of the given Inequation is given by
X < 0 and x > - a -----------> -a < x < 0
Combining two cases together, we get (-a < x < 0) or ( 0 ≤ x < a)
Once we take extreme points, we get –a < x < a
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