The solution of the quadratic inequality x2 x -... - JAMB Mathematics 2007 Question
The solution of the quadratic inequality (x2 + x - 12) \(\geq\) 0 is
A
x \(\geq\) 3 or x \(\geq\) -4
B
x \(\leq\) 3 or x \(\leq\) -4
C
x \(\geq\) 3 or x \(\leq\) -4
D
x \(\geq\) -3 or x \(\leq\) 4
correct option: c
(x2 + x - 12) \(\geq\) 0 , (x - 3)(x + 4) \(\geq\) 0
For the condition to hold, each of (x - 3) and (x + 4) must be of the same sign
.i.e. x - 3 \(\geq\) 0 and x + 4 \(\geq\) 0
or x - 3\(\leq\) 0 and x + 4 \(\leq\) 0
when x \(\geq\) 3, the condition is satisfied
when x \(\geq\) -4, the condition is not satisfied.
when x \(\leq\) 3, the condition is not satisfied
when x \(\leq\) -4 , the condition is not satisfied. Thus, the solution of the inequality is x \(\geq\) 3 or x \(\leq\) -4 ,
For the condition to hold, each of (x - 3) and (x + 4) must be of the same sign
.i.e. x - 3 \(\geq\) 0 and x + 4 \(\geq\) 0
or x - 3\(\leq\) 0 and x + 4 \(\leq\) 0
when x \(\geq\) 3, the condition is satisfied
when x \(\geq\) -4, the condition is not satisfied.
when x \(\leq\) 3, the condition is not satisfied
when x \(\leq\) -4 , the condition is not satisfied. Thus, the solution of the inequality is x \(\geq\) 3 or x \(\leq\) -4 ,
Please share this, thanks:
Add your answer
No responses