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CBSE Class 9 Answered

find the values of a and b so that x+1 and x-1 are factors of x⁴+ax³+x²+2x+b
Asked by shivalaxmi0205 | 15 Feb, 2023, 06:49: PM
answered-by-expert Expert Answer
(x + 1) and (x - 1) are the factors of x to the power of 4 plus a x cubed plus x squared plus 2 x plus b.
Let f(x) = x to the power of 4 plus a x cubed plus x squared plus 2 x plus b
Then f(-1) = 0 and f(1) = 0
That is,
f left parenthesis negative 1 right parenthesis equals open parentheses negative 1 close parentheses to the power of 4 plus a open parentheses negative 1 close parentheses cubed plus open parentheses negative 1 close parentheses squared plus 2 open parentheses negative 1 close parentheses plus b equals 0 1 minus a plus 1 minus 2 plus b equals 0 minus a plus b equals 0 space space space space space space space space space..... left parenthesis 1 right parenthesis f open parentheses 1 close parentheses equals open parentheses 1 close parentheses to the power of 4 plus a open parentheses 1 close parentheses cubed plus open parentheses 1 close parentheses squared plus 2 open parentheses 1 close parentheses plus b equals 0 1 plus a plus 1 plus 2 plus b equals 0 a plus b equals negative 4 space space space space space space space space..... left parenthesis 2 right parenthesis S o l v i n g space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma 2 b equals negative 4 rightwards double arrow b equals negative 2 A n d comma space a plus open parentheses negative 2 close parentheses equals negative 4 rightwards double arrow a equals negative 2
Answered by Rashmi Khot | 16 Feb, 2023, 03:18: PM

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