Short and Simple Cubic

Algebra Level 4

The roots of the polynomial P ( x ) = x 3 + 5 x + 4 P(x) = x^3 + 5x + 4 are r r , s s , and t t . Evaluate ( r + s ) 4 ( s + t ) 4 ( t + r ) 4 (r+s)^4 (s+t)^4 (t+r)^4 .


The answer is 256.

Danish Ahmed by Danish Ahmed , 24, India

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1 solution

Danish Ahmed
Dec 10, 2015

We have r + s + t = 0 r+s+t=0 , and thus ( r + s ) 4 ( s + t ) 4 ( r + t ) 4 = ( − t ) 4 ( − r ) 4 ( − s ) 4 = ( − r s t ) 4 = ( − 4 ) 4 = 256 (r+s)^4(s+t)^4(r+t)^4=(-t)^4(-r)^4(-s)^4=(-rst)^4=(-4)^4=\boxed{256}

11 Helpful 0 Interesting 0 Brilliant 0 Confused

Yep. Same way.

Shreyash Rai - 5 years, 6 months ago

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