Answer:
3
Explanation:
You want the value of 'a' that makes ax⁴ +x³ -x² +3x +2 = 0 and ax⁴ -x² +3x +1 = 0 have a common root.
Common root
The common root will also be a root of the difference of the two equations.
(ax⁴ +x³ -x² +3x +2) -(ax⁴ -x² +3x +1) = 0
x³ +1 = 0
x = -1
Coefficient
For x = -1 to be a root of the second equation, we must have ...
a(1) -(1) +3(-1) +1 = 0 . . . . . . . substitute -1 for x
a - 3 = 0 . . . . . . . . . . simplify
a = 3
The value of 'a' is 3 to make the two equations have a common root.
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