Advertisements
Advertisements
प्रश्न
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)?
Advertisements
उत्तर
We know that,
p(x) = g(x) × q(x) + r(x)
According to the question,
q(x) = 0
When q(x) = 0, then r(x) is also = 0
So, now when we divide p(x) by g(x),
Then p(x) should be equal to zero
Hence, the relation between the degrees of p(x) and g(x) is the degree p(x) < degree g(x).
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
Obtain all other zeroes of 3x4 + 6x3 – 2x2 – 10x – 5, if two of its zeroes are `sqrt(5/3)` and - `sqrt(5/3)`
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)
Give examples of polynomials p(x), g(x), q(x) and r(x), which satisfy the division algorithm
deg q(x) = deg r(x)
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
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) = 4x3 + 8x + 8x2 + 7, g(x) = 2x2 – x + 1
Obtain all zeros of f(x) = x3 + 13x2 + 32x + 20, if one of its zeros is –2.
Obtain all zeros of the polynomial f(x) = x4 − 3x3 − x2 + 9x − 6, if two of its zeros are `-sqrt3` and `sqrt3`
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).
It is given that –1 is one of the zeroes of the polynomial x3 + 2x2 – 11x – 12. Find all the zeroes of the given polynomial.
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)
Which one of the following statements is correct?
Can x2 – 1 be the quotient on division of x6 + 2x3 + x – 1 by a polynomial in x of degree 5?
What will the quotient and remainder be on division of ax2 + bx + c by px3 + qx2 + rx + s, p ≠ 0?
