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

## Roots of equation – PRMO 2017

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

## Check the Answer

But try the problem first…

Answer: is 36.

Source
Suggested Reading

PRMO, 2017, Question 19

Higher Algebra by Hall and Knight

## Try with Hints

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.