There are 2 pairs of numbers: (a,c) & (b,d).

(a,c) is the root of x^2 + ax - b = 0

(b,d) is the root of x^2 + cx + d = 0

Find all possible real values for a, b, c and d.

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- May 30th 2009, 12:30 AMthe undertakeralgebraic equation problem
There are 2 pairs of numbers: (a,c) & (b,d).

(a,c) is the root of x^2 + ax - b = 0

(b,d) is the root of x^2 + cx + d = 0

Find all possible real values for a, b, c and d. - May 30th 2009, 05:13 AMI-ThinkSystems
It's the undertaker. Hi

a and c are the roots of the equation

Then

Equating coefficients

b and d are the roots of the equation

Then

Equating coefficients

We have a system of 4 equations

From (4):

Into (3): and into (1):

(2) into (1):

Hence c

Into (4):

N.B. When choosing values to input into the equation, if you let one of a,c,d be positive, then all the others have to be positive and vice-versa.

Possible values

- May 30th 2009, 06:11 AMCaptainBlack