Advertisements
Advertisements
प्रश्न
What will the quotient and remainder be on division of ax2 + bx + c by px3 + qx2 + rx + s, p ≠ 0?
Advertisements
उत्तर
Degree of the polynomial px3 + qx2 + rx + s is 3
Degree of the polynomial ax2 + bx + c is 2
Here, degree of px3 + qx2 + rx + s is greater than degree of the ax2 + bx + c
Therefore, the quotient would be zero
And the remainder would be the dividend = ax2 + bx + c.
APPEARS IN
संबंधित प्रश्न
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following
p(x) = x3 – 3x2 + 5x – 3, g(x) = x2 – 2
Divide the polynomial p(x) by the polynomial g(x) and find the quotient and remainder in each of the following
p(x) = x4 – 5x + 6, g(x) = 2 – x2
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial
x2 + 3x + 1, 3x4 + 5x3 – 7x2 + 2x + 2
On dividing x3 – 3x2 + x + 2 by a polynomial g(x), the quotient and remainder were x – 2 and –2x + 4, respectively. Find g(x)
If the polynomial x4 – 6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 – 2x + k, the remainder comes out to be x + a, find k and a.
Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following:
f(x) = 10x4 + 17x3 – 62x2 + 30x – 3, g(x) = 2x2 + 7x + 1
Check whether the first polynomial is a factor of the second polynomial by applying the division algorithm:
g(x) = 2x2 – x + 3, f(x) = 6x5 – x4 + 4x3 – 5x2 – x – 15
What must be subtracted from the polynomial f(x) = x4 + 2x3 − 13x2 − 12x + 21 so that the resulting polynomial is exactly divisible by x2 − 4x + 3 ?
Verify division algorithm for the polynomial f(x)= (8 + 20x + x2 – 6x3) by g(x) = (2 + 5x – 3x2).
If (x + a) is a factor of (2x2 + 2ax + 5x + 10), then find the value of a.
If (a – b), a and (a + b) are zeros of the polynomial 2x3 – 6x2 + 5x – 7, write the value of a.
Find the quotient and remainder of the following.
(4x3 + 6x2 – 23x + 18) ÷ (x + 3)
Find the quotient and remainder of the following.
(8y3 – 16y2 + 16y – 15) ÷ (2y – 1)
The area of a rectangle is x2 + 7x + 12. If its breadth is (x + 3), then find its length
The sum of (x + 5) observations is (x3 + 125). Find the mean of the observations
If on division of a polynomial p(x) by a polynomial g(x), the quotient is zero, what is the relation between the degrees of p(x) and g(x)?
Find k so that x2 + 2x + k is a factor of 2x4 + x3 – 14 x2 + 5x + 6. Also find all the zeroes of the two polynomials.
For which values of a and b, are the zeroes of q(x) = x3 + 2x2 + a also the zeroes of the polynomial p(x) = x5 – x4 – 4x3 + 3x2 + 3x + b? Which zeroes of p(x) are not the zeroes of q(x)?
