Q55 / 160 · AP EAMCET 2020 (21 Sep Shift 2) · Mathematics

If a Polynomial $x^4+x^2+1$ is divisible by $x^2+m x+1$ and $x^2+n x+1$. Then $m+n$ is equal to (1) 2 (2) 0 (3) 3 (4) 4

  • A
    2
  • Correct answer
    B
    0
  • C
    3
  • D
    4

Solution

$x^4+x^2+1$ is divisible by $x^2+n x+1$ and $x^2+m x+1$ $$ \therefore x^4+x^2+1=\left(x^2+m x+1\right)\left(x^2+n x+1\right) $$ equating the coefficients of $x^3$ on both sides $$ m+n=0 $$

Hence, the correct answer is option: 'B'.

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