Factor each Polynomial
2 answers:
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Answer:
A = 68 unit^2
Step-by-step explanation:
Given:-
The piece-wise function f(x) is defined over an interval as follows:
f(x) = { x^2+3x+4 , x < 3
f(x) = { x^2+3x+4 , x≥3
Domain : [ -3 , 4 ]
Find:-
Find the area of the region enclosed by f(x) and the x axis
Solution:-
- The best way to tackle problems relating to piece-wise functions is to solve for each part individually and then combine the results.
- The first portion of function is valid over the interval [ -3 , 3 ]:
- The area "A1" bounded by f(x) is given as:
Where, The interval of the function { -3 , 3 ] = [ a , b ]:
- Similarly for the other portion of piece-wise function covering the interval [3 , 4] :
- The area "A2" bounded by f(x) is given as:
Where, The interval of the function { 3 , 4 ] = [ a , b ]:
- The total area "A" bounded by the piece-wise function over the entire domain [ -3 , 4 ] is given:
A = A1 + A2
A = 42 + 26
A = 68 unit^2
Answer: 24
<u>Step-by-step explanation:</u>
Let's find one solution:
3x² + 7x + c = 0
a=3 b=7 c=c
First, let's find c so that it has REAL ROOTS.
⇒ Discriminant (b² - 4ac) ≥ 0
7² - 4(3)c ≥ 0
49 - 12c ≥ 0
-12c ≥ -49
Since c must be a positive integer, 1 ≤ c ≤ 4
Example: c = 4
3x² + 7x + 4 = 0
(3x + 4)(x + 1) = 0
x = -4/3, x = -1 Real Roots!
<em>You need to use Quadratic Formula to solve for c = {1, 2, 3}</em>
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Valid solutions for c are: {1, 2, 3, 4)
Their product is: 1 x 2 x 3 x 4 = 24
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