Question

The polynomial which when divided by −x² + x − 1 gives a quotient x − 2 and remainder 3, is

पर्याय

• x³ − 3x² + 3x − 5

• −x³ − 3x² − 3x − 5

• −x³ + 3x² − 3x + 5

• x³ − 3x² − 3x + 5

Answer 1

We know that

`f(x)= g (x)q(x)+ r(x)`

`= (- x^2 + x -1)(x - 2 + 3)`

`= - x^3 + x^2 - x+ 2x^2 - 2x + 2 + 3`

`= - x^3 + x^2 - 2x^2 - x - 2x + 2 + 3`

` = - x^3 + 3x^2 - 3x + 5`Therefore,

 

The polynomial which when divided by `- x^2 + x -1` gives a quotient  `x -2` and remainder 3, is`- x^2 + 3x^2 - 3x + 5`

Hence, the correct choice is `(c).`