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.
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