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Truman
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.
\[2+ \sqrt{5} and 2 - \sqrt{5}\]
equation bcam x^2 - (a+b)x+ a.b =0 take a=2+sqr 5 , b=2-sqr -5
\[x ^{2} - (a+b)x + ab = 0?\]
this is from an example in my book, but I don't understand the example:
tis what any quarratic equation can be form...
if their two roots are given .got it ...now
that's the example from the book
yea ........now plug in...
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.
that's the books example typed out,
thank you, i'm trying it