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Truman

  • 4 years ago

Find the quadratic equation whose solutions are: 2 + sqr(5) and 2 - sqr(5) I'm not just looking for an answer but rather to learn.

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  1. Truman
    • 4 years ago
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    \[2+ \sqrt{5} and 2 - \sqrt{5}\]

  2. amitlpu91
    • 4 years ago
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    equation bcam x^2 - (a+b)x+ a.b =0 take a=2+sqr 5 , b=2-sqr -5

  3. Truman
    • 4 years ago
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    \[x ^{2} - (a+b)x + ab = 0?\]

  4. Truman
    • 4 years ago
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    this is from an example in my book, but I don't understand the example:

  5. amitlpu91
    • 4 years ago
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    tis what any quarratic equation can be form...

  6. amitlpu91
    • 4 years ago
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    if their two roots are given .got it ...now

  7. Truman
    • 4 years ago
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    |dw:1326657719757:dw|

  8. Truman
    • 4 years ago
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    that's the example from the book

  9. amitlpu91
    • 4 years ago
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    yea ........now plug in...

  10. imperialist
    • 4 years ago
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    If you are given 2 (or more than 2, it doesn't matter) roots of a polynomial, say a and b in this case, then that just means if you were to factor your polynomial, you would get \[f(x)=(x-a)(x-b)\] By multiplying this together, you get the equation \[x^2-(a+b)+ab\] Thus, in your example, you would just plug in \[a=2+\sqrt{5}, b=2-\sqrt{5}\] to the above equation to reach your answer.

  11. Truman
    • 4 years ago
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    |dw:1326657923682:dw|

  12. Truman
    • 4 years ago
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    that's the books example typed out,

  13. Truman
    • 4 years ago
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    thank you, i'm trying it

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