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

Key Concepts


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.

Subscribe to Cheenta at Youtube