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Find all the values of a for which the equations

x^2 + ax + 1 = 0

x^2 - 3x - a = 0

 

have a common real root. Enter all the possible values, separated by commas.

 Jan 27, 2022
 #1
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in order for the first one to be real, you would need

(x+1)(x+1) where a is 2

or (x-1)(x-1) where a is -2

 

putting in 2 for a in the second equation is not a real root

putting -2 for a in the second equation gives us

(x-2)(x-1)

 

this if a=-2 then x=1 is the common root

 Jan 27, 2022

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