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CBSE Class 10 Answered

find all the zeroes of x to the power4 -6x cube -26 x square +138x -35 if two zeroes are 2+ ,-  root 3
Asked by ajayrath7 | 16 Mar, 2019, 08:42: AM
answered-by-expert Expert Answer
This question can be solved only if we assume the given polynomial is :-  p(x) = x4 -6x3 -26x2 +140x -35
 
let α = 2+√3   and  β = 2-√3  are roots of p(x). Then (x-α)(x-β) = x2 -(α+β)x + (αβ) = x2 -4x +1  is the factor of p(x)
 
If we divide p(x) by x2 -4x +1 we get quotient (x2 -2x + 35) . This quotient is factorised as (x-7)(x+5)
 
Hence other roots are 7 and -5
Answered by Thiyagarajan K | 16 Mar, 2019, 11:03: AM
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