please help me with this question

for which real values of b do the equations

x^3 + bx^2 + 2bx -1 =0 and x^2 + (b-1)x + b = 0

have a common root

thank you

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- Sep 6th 2007, 06:10 AMieatfoodfinding common roots
please help me with this question

for which real values of b do the equations

x^3 + bx^2 + 2bx -1 =0 and x^2 + (b-1)x + b = 0

have a common root

thank you - Sep 6th 2007, 07:26 AMred_dog
Let be the common root.

We observe that .

Multiplying (2) by and then substracting from (1), we have

(3)

The equality (2) can be written as

Using (3) we have .

Plug in (2) and we have .

If , the common root is .

If , the common root is .