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CBSE Class 9 Answered

find the value of a and b so that x+1and x-1 are the the factor of x^4+ax^3+2x^-3x+b
Asked by jhanvi3824 | 07 Oct, 2023, 09:35: PM
answered-by-expert Expert Answer
 
begin mathsize 14px style f left parenthesis x right parenthesis space equals space x to the power of 4 plus a x cubed plus 2 x squared minus 3 x plus b end style
 
If (x+1) is a factor of f(x) , then f(-1) = 0
 
begin mathsize 14px style f left parenthesis negative 1 right parenthesis space equals space 1 minus a space plus 2 space plus 3 space plus space b space equals space 0 end style
 
Hence , we get ,   begin mathsize 14px style negative a space plus space b space equals space minus 6 end style .................... (1)
 
If (x-1) is a factor of f(x) , then f(1) = 0
 
begin mathsize 14px style f left parenthesis 1 right parenthesis space equals space 1 space plus a space plus 2 space minus 3 space plus b space space equals space 0 end style
 
Hence , we get , begin mathsize 14px style a plus b space equals space 0 end style ..........................(2)
 
hence we get , a = 3 and b = -3
Answered by Thiyagarajan K | 08 Oct, 2023, 11:17: AM
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