Answer:
Step-by-step explanation:
Given is a function as 
Equating to 0 we have equation
If the function f(x) has x intercepts then the solutions are real
Let us use remainder theorem and change of signs rule
f(0) = 1>0
f(-1) = -1+3+1=3
f(-2) = -32+6+1<0
This implies there is a real root between -1 and -2.
f(1) = -1
Since f(0) and f(1) have different signs, there exists a real root between 0 and 1.
f(2) = 32-6+1>0
Since f(1) and f(2) have different signs there exists a real root between 1 and 2.
Thus there are definitely three real solutions as
one between -1 and 0, one between 0 and 1, and third between 1 and 2.
Answer:
p > 10.67
Step-by-step explanation:
Given the inequality -1 1/2p < -16
Before we can represent the inequality on a graph we just simplify it first. On simplification:
-1 1/2p < -16
(-3/2)p < -16
Multiplying both sides by 2
-3p < -32
Dividing both sides by -3 will change the sense of the inequality as shown:
p > -32/-3
p > 32/3
p > 10.67
Find the graph of the resulting inequality in the attachment.
The expression equivalent to <span> ^4 sqrt 144a^12 b^3 will be found by simplifying our expression as follows:
</span><span> ^4 sqrt 144a^12 b^3
=(144a^12b^3)^(1/4)
=(12^2a^12b^3)^(1/4)
=12^(1/4*2)a^(12*1/4)b^(3*1/4)
=12^(1/2)a^3b^(3/4)
Answer: </span>12^(1/2)a^3b^(3/4)
This would be written as:
4(n-11)