If x-1 and x-1 are factors of m x3-x2-2 x-n find the value of m and n

(x 1) and (x+1) are factors of the given polynomial. (x 1) = 0 → x=1 (x+1) = 0 → x= 1 Put x = 1 mx³+x² 2x+n m(1)³+(1)² 2(1)+n = 0 m(1)+1 2+n = 0 a 1+b = ...

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Standard IX

Mathematics

Factorisation of a Polynomial

If x+1 and x-...

Question

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

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Solution

Let, f(x)= $m x^{3} + x^{2} - 2 x + n$
Since (x+1) is a factor of f(x),
then f(−1)=0
⇒ −m+1+2+n=0
⇒ m−n=3........(1)
Since (x−1) is a factor of f(x),
then f(1)=0
⇒ m+1−2+n=0
⇒ m+n=1.........(2)
Solving from (1) and (2) we get m=2 and n=(−1)

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

Let, f(x)= mx3+x2−2x+n Since (x+1) is a factor of f(x), then f(−1)=0⇒ −m+1+2+n=0⇒ m−n=3........(1)Since (x−1) is a factor of f(x),then f(1)=0⇒ m+1−2+n=0⇒ m+n=1.........(2)Solving from (1) and (2) we get m=2 and n=(−1)

Let, f(x)= $m x^{3} + x^{2} - 2 x + n$
Since (x+1) is a factor of f(x),
then f(−1)=0
⇒ −m+1+2+n=0
⇒ m−n=3........(1)
Since (x−1) is a factor of f(x),
then f(1)=0
⇒ m+1−2+n=0
⇒ m+n=1.........(2)
Solving from (1) and (2) we get m=2 and n=(−1)