Question

If (x +1) and (x – 1) are factors of mx³ +x² -2x + n, find the value of
m and n.

Answer 1

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Here is your answer,

In attachment

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Answer 2

Heya !!!





Given that,



( X + 1 ) and ( X - 1) are factor of the given polynomial.






So,




( X +1 ) = 0 OR ( X -1) = 0



X = -1 OR X = 1




P(X) = MX³ + X² - 2X + N




P(-1) = M × (-1)³ + (-1)² - 2 × -1 + N





=> M × -1 + 1 + 2 + N = 0






=> -M + 3 + N = 0




=> M - N = 3 -----------(1)





And,




P(1) = M × (1)³ + (1)² - 2 × 1 + N







=> M + 1 - 2 + N = 0





=> M + N = 1 --------(2)




From equation (1) we get,




M - N = 3





M = 3 + N ---------(3)




Putting the value of M in equation (2)




M + N = 1




3 + N + N = 1




2N = 1-3




2N = -2




N = -2/2




N = -1





Putting the value of N in equation (3)





M = 3 + N



M = 3+(-1) = 2.





Hence,




M = 2 and N = -1





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