Advertisements
Advertisements
प्रश्न
If the polynomials az3 + 4z2 + 3z – 4 and z3 – 4z + a leave the same remainder when divided by z – 3, find the value of a.
Advertisements
उत्तर
Let p1(z) = az3 + 4z2 + 3z – 4 and p2(z) = z3 – 4z + 0
When we divide p1(z) by z – 3, then we get the remainder p,(3).
Now, p1(3) = a(3)3 + 4(3)2 + 3(3) – 4
= 27a + 36 + 9 – 4
= 27a + 41
When we divide p2(z) by z – 3 then we get the remainder p2(3).
Now, p2(3) = (3)3 – 4(3) + a
= 27 – 12 + a
= 15 + a
According to the question,
Both the remainders are same.
p1(3) = p2(3)
27a + 41 = 15 + a
27a – a = 15 – 41
26a = –26
a = `(-26)/26`
a = –1
APPEARS IN
संबंधित प्रश्न
Find the remainder when x3 + 3x2 + 3x + 1 is divided by x + π.
Using the Remainder Theorem, factorise the following completely:
3x3 + 2x2 – 19x + 6
Find the value of a, if the division of ax3 + 9x2 + 4x – 10 by x + 3 leaves a remainder 5.
The polynomials ax3 + 3x2 – 3 and 2x3 – 5x + a, when divided by x – 4, leave the same remainder in each case. Find the value of a.
Divide the first polynomial by the second polynomial and find the remainder using remainder theorem.
(54m3 + 18m2 − 27m + 5) ; (m − 3)
Find the values of a and b when the polynomials f(x)= 2x2 -5x +a and g(x)= 2x2 + 5x +b both have a factor (2x+1).
Check whether p(x) is a multiple of g(x) or not
p(x) = x3 – 5x2 + 4x – 3, g(x) = x – 2
By remainder theorem, find the remainder when, p(x) is divided by g(x) where, p(x) = x3 – 2x2 – 4x – 1; g(x) = x + 1
If x51 + 51 is divided by x + 1, the remainder is ______.
By Remainder Theorem find the remainder, when p(x) is divided by g(x), where p(x) = x3 – 3x2 + 4x + 50, g(x) = x – 3
