The condition that a root of the equation http://asset2.texhub.com/b/IGF4XjIgKyBieCArIGMgPSAwIA== may be reciprocal to a root of http://asset1.texhub.com/b/IGFfMXheM...BjXzEgPSAwIA== is

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- Jun 29th 2012, 12:33 PMswordfish774relationship between coefficients of a quadratic equations
The condition that a root of the equation http://asset2.texhub.com/b/IGF4XjIgKyBieCArIGMgPSAwIA== may be reciprocal to a root of http://asset1.texhub.com/b/IGFfMXheM...BjXzEgPSAwIA== is

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- Jun 29th 2012, 04:24 PMSorobanRe: relationship between coefficients of a quadratic equations
Hello, swordfish774!

Quote:

. . . . Are they kidding?

.[1]

. . .[2]

Equating [1] and [2], we have: .

Multiply (a) and (b): .

Multiply (b) and (c): .

Multiply (a) and (c): .

Square (f): .

Multiply (e) and (d):. .

Therefore, (g) = (h): .

- Jun 29th 2012, 06:20 PMswordfish774Re: relationship between coefficients of a quadratic equations
What are the curly brackets? How did you know that a=c1, b= b1, c=a1 for sure?

- Jun 29th 2012, 10:55 PMbiffboyRe: relationship between coefficients of a quadratic equations
This reminds me of a similar question: If p and q are rhe roots of ax^2+bx+c=0 find the equation whose roots are 1/p and 1/q

We have p+q=-b/a and pq=c/a So 1/p+1/q=(q+p)/pq=(-b/a)/(c/a)=-b/c and (1/p)*(1/q)=1/pq=a/c

So required equation is x^2+(b/c)x+(a/c)=0 That is cx^2+bx+a=0 - Jul 1st 2012, 04:01 AMswordfish774Re: relationship between coefficients of a quadratic equations