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Try this beautiful problem from the Pre-RMO, 2017 based on roots of equation.

Suppose 1,2,3 are roots of the equation \(x^{4}+ax^{2}+bx=c\). Find the value of c.

- is 107
- is 36
- is 840
- cannot be determined from the given information

Roots

Equations

Algebra

But try the problem first...

Answer: is 36.

Source

Suggested Reading

PRMO, 2017, Question 19

Higher Algebra by Hall and Knight

First hint

1,2,3 are the roots of \(x^{4}+ax^{2}+bx-c=0\)

Second Hint

since sum of roots=0 fourth root=-6 by using Vieta's formula

Final Step

c=36.

- https://www.cheenta.com/rational-number-and-integer-prmo-2019-question-9/
- https://www.youtube.com/watch?v=lBPFR9xequA

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