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Complex Roots Unleashed (Posted on 2024-04-23)

A complex number a≠-1 is the root of an equation x³+1=0.

Find 1+2a+3a²+4a³+5a⁴.

No Solution Yet Submitted by Danish Ahmed Khan

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Puzzle Answer

| Comment 1 of 7

a^3+1 =0

=> (a+1)(a^2-a+1)=0

=> a^2-a+1=0, since a≠-1.

Now, 5*a^4+4*a^3+3*a^2+2a+1 = (5a^2+9a+7)(a^2-a+1)-6

Since, a^2-a+1 =0, it follows that the value of the given expression is -6.

Posted by K Sengupta on 2024-04-23 08:39:28

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