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If the equations ax^4+x³-x² + 3x + 2 = 0 and ax^4-x²+3x+1=0 have a common root, then find the value of a.​

User VsMaX
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7 votes

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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If the equations ax^4+x³-x² + 3x + 2 = 0 and ax^4-x²+3x+1=0 have a common root, then-example-1
User Irreal
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