David's phone bill each month is $30. He is also charged $0.10 per GB of data he uses. If his phone bill in july was $42, how ma
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Answer:
(a)
(b) Proved
Step-by-step explanation:
Given
--- the root
Solving (a): The polynomial
A cubic function is represented as:
Expand
Rewrite as:
The root is represented as:
By comparison:
So, we have:
Expand
Evaluate like terms
Recall that:
So, we have:
Equate to 0
Rewrite as:
Express as a cubic function
Hence, the cubic polynomial is:
Solving (b): Prove that r is irrational
The constant term of is -6
The divisors of -6 are: -6,-3,-2,-1,1,2,3,6
Calculate f(x) for each of the above values to calculate the remainder when f(x) is divided by any of the above values
For r to be rational;
The divisors of -6 must divide f(x) without remainder
i.e. Any of the above values must equal 0
<em>Since none equals 0, then r is irrational</em>