SOLUTION: a) How many solutions can an equation whose form is (x-1)(x –2)(x – 3) = 0 have?
b) Can you use the information you obtained in part a) and generalize how many maximum solu
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Rational-functions
-> SOLUTION: a) How many solutions can an equation whose form is (x-1)(x –2)(x – 3) = 0 have?
b) Can you use the information you obtained in part a) and generalize how many maximum solu
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Question 254719: a) How many solutions can an equation whose form is (x-1)(x –2)(x – 3) = 0 have?
b) Can you use the information you obtained in part a) and generalize how many maximum solutions you would expect in each of the following four cases? How? (Do NOT try to solve the following equations):
i. x4 +x3+ x2+ x +x0 = 0
ii. x54 +x12 + x11 + x10 + 23 = 0
iii. x99 +x98 +x97 + ….. + x3 + x2 + x1 + x0 = 0
iv. x34 + x32 + 1 = 0
You can put this solution on YOUR website! a) How many solutions can an equation whose form is (x-1)(x –2)(x – 3) = 0 have?
ANSWER -> using the zero product property, we will get 3 answers: 1, 2, and 3.
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b) Can you use the information you obtained in part a) and generalize how many maximum solutions you would expect in each of the following four cases? How? (Do NOT try to solve the following equations):
i. x^4 +x^3+ x^2+ x^1 +x^0 = 0
ANSWER -> There will be at most 4 solutions
ii. x^54 +x^12 + x^11 + x^10 + 23 = 0
ANSWER -> There will be at most 54 solutions
iii. x^99 +x^98 +x^97 + ….. + x^3 + x^2 + x^1 + x^0 = 0
ANSWER -> There will be at most 99 solutions
iv. x^34 + x^32 + 1 = 0
ANSWER -> There will be at most 34 solutions.
IN general the maximum number of solutions will be the largest degree of the polynomial.
You can put this solution on YOUR website! a) How many solutions can an equation whose form is (x-1)(x –2)(x – 3) = 0 have?
Ans: 3 ; x = 1,2,or 3
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b) Can you use the information you obtained in part a) and generalize how many maximum solutions you would expect in each of the following four cases? How? (Do NOT try to solve the following equations):
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Rule: The highest power term determines the number of solutions.
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i. x4 +x3+ x2+ x +x0 = 0
Ans: 4
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ii. x54 +x12 + x11 + x10 + 23 = 0
Ans: 54
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I think you can see the other oanswers.
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Cheers,
Stan H.
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iii. x99 +x98 +x97 + ….. + x3 + x2 + x1 + x0 = 0
iv. x34 + x32 + 1 = 0
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