Maths-
General
Easy

Question

If alpha comma beta comma gamma comma delta are roots of x to the power of 4 minus 100 x cubed plus 2 x squared plus 4 x plus 10 equals 0 , then 1 over alpha plus 1 over beta plus 1 over gamma plus 1 over delta is equal to-

  1. 2/5    
  2. fraction numerator 1 over denominator 10 end fraction    
  3. 4    
  4. -2/5    

hintHint:

We know that in equation given in the question, x to the power of 4 minus 100 x cubed plus 2 x squared plus 4 x plus 10 space equals space 0  if alpha comma beta comma gamma comma delta are the roots, then,'
alpha plus beta plus gamma plus delta = negative fraction numerator left parenthesis c o e f f i c i e n t space o f space x cubed right parenthesis over denominator left parenthesis c o e f f i c i e n t space o f space x to the power of 4 right parenthesis end fractionequals negative fraction numerator negative 100 over denominator 1 end fraction equals 100
alpha beta plus beta gamma plus gamma delta plus delta alpha = fraction numerator left parenthesis c o e f f c i e n t space o f space x squared right parenthesis over denominator left parenthesis c o e f f i c i e n t space o f space x to the power of 4 right parenthesis end fraction equals 2 over 1 equals 2
alpha beta gamma plus beta gamma delta plus gamma delta alpha plus delta alpha beta = negative fraction numerator left parenthesis c o e f f i c i e n t space o f space x right parenthesis over denominator left parenthesis c o e f f i c i e n t space o f space x to the power of 4 right parenthesis end fractionequals negative 4 over 1 equals negative 4
alpha beta gamma deltaequals fraction numerator c o n s tan t space t e r m over denominator left parenthesis c o e f f i c i e n t space o f space x to the power of 4 right parenthesis end fraction equals 10 over 1 equals 10

The correct answer is: -2/5


    Step by step solution:
    1 over alpha plus 1 over beta plus 1 over gamma plus 1 over delta = fraction numerator beta gamma delta plus alpha gamma delta plus alpha beta delta plus alpha beta gamma over denominator alpha beta gamma delta end fraction equals fraction numerator negative 4 over denominator 10 end fraction equals space minus space 2 over 5
    (we got the results as shown in the hints)
    Hence, option(a) is the correct option.

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