Brain hammering question!

Calculus Level 5

If the equation ${ x }^{ 6 }-{ 54x }^{ 5 }+{ 1215x }^{ 4 }+{ 20cx }^{ 3 }+{ 15dx }^{ 2 }+{ 6ex }+{ f }=0$ has $6$ real roots, find the value of $c+d+e+f$ .

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The answer is 478224.

1 solution

Aditya Kumar
May 6, 2015

Sorry for using calculus for this question. Find the 4th derivative of the eqn. You'll see that the roots repeat. Now take the 3rd derivative and find the value of 'c'. Repeat this for all!

It's root's are 9 , 9 , 9 , 9 , 9 ,9

So answer is -9^3+9^4-9^5+9^6 . which is positive ! But you given negative answer .

Btw no need to use calculus , you see there is sum of root's taken one at a time is equal to 2 at a time . Hence root's should be equal .

Nishu sharma - 6 years, 1 month ago

@Nishu sharma the answer comes out to be negative. Can you post your solution?

Aditya Kumar - 6 years, 1 month ago

Thanks. I have updated the answer accordingly.

In future, if you spot any errors with a problem, you can “report” it by selecting "report problem" in the “dot dot dot” menu in the lower right corner. This will notify the problem creator who can fix the issues.

Calvin Lin Staff - 6 years, 1 month ago

Calvin Lin sir the updated app doesn't show the points of a question. Can you please work on it?