Advertisements
Advertisements
Question
Find the quotient and the remainder when f(x) = x4 – 3x2 + 4x + 5 is divided by g(x) = x2 – x + 1.
Advertisements
Solution
x2 + x – 3
`x^2 - x + 1")"overline(x^4 + 0x^3 - 3x^2 + 4x + 5)`
x4 – x3 + x2
– + –
x3 – 4x2 + 4x + 5
x3 – x2 + x
– + –
–3x2 + 3x + 5
–3x2 + 3x – 3
+ – +
8
Quotient q(x) = x2 + x – 3
Remainder r(x) = 8
APPEARS IN
RELATED QUESTIONS
Find the zeros of the quadratic polynomial 4x2 - 9 and verify the relation between the zeros and its coffiecents.
Find the zeros of the quadratic polynomial 9x2 - 5 and verify the relation between the zeros and its coefficients.
if α and β are the zeros of ax2 + bx + c, a ≠ 0 then verify the relation between zeros and its cofficients
Verify that the numbers given along side of the cubic polynomials are their zeroes. Also verify the relationship between the zeroes and the coefficients.
`2x^3 + x^2 – 5x + 2 ; 1/2, 1, – 2`
Find the zeroes of the following quadratic polynomial and verify the relationship between the zeroes and the coefficients.
6x2 – 3 – 7x
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
`-1/4 ,1/4`
Find a quadratic polynomial with the given numbers as the sum and product of its zeroes respectively.
4, 1
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `1/alpha-1/beta`
By actual division, show that x2 – 3 is a factor of 2x4 + 3x3 – 2x2 – 9x – 12.
If 2 and -2 are two zeroes of the polynomial `(x^4 + x^3 – 34x^2 – 4x + 120)`, find all the zeroes of the given polynomial.
If α, β are the zeroes of the polynomial f(x) = 5x2 – 7x + 1 then `1/α + 1/β = ?`
If α, β, γ are are the zeros of the polynomial f(x) = x3 − px2 + qx − r, the\[\frac{1}{\alpha\beta} + \frac{1}{\beta\gamma} + \frac{1}{\gamma\alpha} =\]
The polynomial which when divided by −x2 + x − 1 gives a quotient x − 2 and remainder 3, is
The below picture are few natural examples of parabolic shape which is represented by a quadratic polynomial. A parabolic arch is an arch in the shape of a parabola. In structures, their curve represents an efficient method of load, and so can be found in bridges and in architecture in a variety of forms.
If the sum of the roots is –p and the product of the roots is `-1/"p"`, then the quadratic polynomial is:
If one of the zeroes of the quadratic polynomial (k – 1)x2 + k x + 1 is –3, then the value of k is ______.
If one of the zeroes of the cubic polynomial x3 + ax2 + bx + c is –1, then the product of the other two zeroes 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.
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.
`(-8)/3, 4/3`
A quadratic polynomial the sum and product of whose zeroes are – 3 and 2 respectively, is ______.
The zeroes of the polynomial p(x) = 2x2 – x – 3 are ______.
