anonymous
  • anonymous
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.
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
\[2+ \sqrt{5} and 2 - \sqrt{5}\]
anonymous
  • anonymous
equation bcam x^2 - (a+b)x+ a.b =0 take a=2+sqr 5 , b=2-sqr -5
anonymous
  • anonymous
\[x ^{2} - (a+b)x + ab = 0?\]

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anonymous
  • anonymous
this is from an example in my book, but I don't understand the example:
anonymous
  • anonymous
tis what any quarratic equation can be form...
anonymous
  • anonymous
if their two roots are given .got it ...now
anonymous
  • anonymous
|dw:1326657719757:dw|
anonymous
  • anonymous
that's the example from the book
anonymous
  • anonymous
yea ........now plug in...
anonymous
  • anonymous
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.
anonymous
  • anonymous
|dw:1326657923682:dw|
anonymous
  • anonymous
that's the books example typed out,
anonymous
  • anonymous
thank you, i'm trying it

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