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notsponge [240]
3 years ago
8

The polynomial of degree 4, P ( x ) has a root of multiplicity 2 at x = 4 and roots of multiplicity 1 at x = 0 and x = − 1 . It

goes through the point ( 5 , 9 ) . Find a formula for P ( x ) .
Mathematics
1 answer:
Svetlanka [38]3 years ago
4 0

To have roots as described, that means we have the following factors: From multiplicity 2 at x=1 has (x-1)^2 as its factor From multiplicity 1 at x=0 has x as a factor From multiplicity 1 at x = -4 has a factor of x+4 Putting these together we get that P(x) = A (x) (x+4) (x-1)^2 Multiply these out and find P(x) = A (x^2 + 4x) (x^2 - 2x + 1) A ( x^4 - 2x^3 + x^2 + 4x^3 - 8x^2 + 4x ) Combine like terms and find P(x) = A (x^4 + 2x^3 - 7x^2 + 4x) To find A, we use the point they gave us (5, 72) P(5) = A [ (5)^4 + 2(5)^3 - 7(5)^2 + 4(5) ] = 72 A [ 625 + 250 - 175 + 20 ] = 72 A [ 720 ] = 72 Divide both sides by 720 and find that A = 0.1 Final answer: P(x) = 0.1 ( x^4 + 2x^3 - 7x^2 + 4x) or P(x) = 0.1 x^4 + 0.2 x^3 - 0.7x^2 + 0.4x

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Line A goes through the points (1, 5) and (-1, 9). Line B goes through the points (0, 2) and (4, -6). Which of the following sta
Delvig [45]
B is correct. Explanation Below:
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Line A never intersects Line B, as they are parallel lines-the slopes are the same-and parallel lines never intersect. 
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pashok25 [27]

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Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Principal = $ 17,500

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Time = 10 years = 20 semesters

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Let's use the formula of the Future Value, to calculate it for this investment:

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3 years ago
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