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CBSE Class 10 Answered

  If the roots of equation x3−12x2+39x−28=0 are in A.P, then common difference will be
Asked by rushabh123 | 18 Feb, 2019, 11:05: AM
answered-by-expert Expert Answer
Let f(x) = x3 -12x2 +39x -28 = 0
 
let us put x=1 , in above function
 
then f(1) = 1 -12 +39 -28 = 0.  Hence (x-1) is a factor of f(x)
 
when f(x) is divided by (x-1), we get quotient (x2 -11x +28) and this quotient is further factorised as (x-4)(x-7)
 
Hence f(x) = (x-1)(x-4)(x-7) = 0
 
Hence roots are 1, 4, 7 which are in arithmetic progression. first term is 1 and common difference is 3
Answered by Thiyagarajan K | 18 Feb, 2019, 11:40: AM
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