Advertisements
Advertisements
Question
The polynomial which when divided by −x2 + x − 1 gives a quotient x − 2 and remainder 3, is
Options
x3 − 3x2 + 3x − 5
−x3 − 3x2 − 3x − 5
−x3 + 3x2 − 3x + 5
x3 − 3x2 − 3x + 5
Advertisements
Solution
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).`
APPEARS IN
RELATED QUESTIONS
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`q(x)=sqrt3x^2+10x+7sqrt3`
If α and β are the zeroes of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/(aalpha+b)+1/(abeta+b)`.
If a and are the zeros of the quadratic polynomial f(x) = 𝑥2 − 𝑥 − 4, find the value of `1/alpha+1/beta-alphabeta`
If 𝛼 and 𝛽 are the zeros of the quadratic polynomial p(x) = 4x2 − 5x −1, find the value of α2β + αβ2.
Find the zeroes of the quadratic polynomial `4x^2 - 4x + 1` and verify the relation between the zeroes and the coefficients.
Find a cubic polynomial whose zeroes are 2, -3and 4.
By actual division, show that x2 – 3 is a factor of` 2x^4 + 3x^3 – 2x^2 – 9x – 12.`
If 3 and –3 are two zeroes of the polynomial `(x^4 + x^3 – 11x^2 – 9x + 18)`, find all the zeroes of the given polynomial.
If two of the zeros of the cubic polynomial ax3 + bx2 + cx + d are each equal to zero, then the third zero is
If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`4x^2 + 5sqrt(2)x - 3`
For the following, find a quadratic polynomial whose sum and product respectively of the zeroes are as given. Also find the zeroes of these polynomials by factorisation.
`21/8, 5/16`
The zeroes of the quadratic polynomial x2 + 99x + 127 are ______.
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`y^2 + 3/2 sqrt(5)y - 5`
Find the zeroes of the quadratic polynomial 6x2 – 3 – 7x and verify the relationship between the zeroes and the coefficients.
If α and β are the zeros of a polynomial f(x) = px2 – 2x + 3p and α + β = αβ, then p is ______.
If one zero of the polynomial p(x) = 6x2 + 37x – (k – 2) is reciprocal of the other, then find the value of k.
Find the sum and product of the roots of the quadratic equation 2x2 – 9x + 4 = 0.
The zeroes of the polynomial p(x) = 25x2 – 49 are ______.
