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.
Roots
Equations
Algebra
But try the problem first...
Answer: is 36.
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.
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.
Roots
Equations
Algebra
But try the problem first...
Answer: is 36.
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.
