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.
Solution:
Given, the polynomials are az³ + 4z² + 3z - 4 and z³ - 4z + a.
The polynomials leave the same remainder when divided by z - 3.
We have to find the value of a.
Let p(x) = az³ + 4z² + 3z - 4
g(x) = z - 3
Now g(x) = 0
z - 3 = 0
z = 3
Put z = 3 in p(x),
p(3) = a(3)³ + 4(3)² + 3(3) - 4
= 27a + 4(9) + 9 - 4
= 27a + 36 + 5
= 27a + 41
Let q(x)= z³ - 4z + a
Put z = 3 in q(x),
q(3) = (3)³ - 4(3) + a
= 27 - 12 + a
= 15 + a
Given, remainder of p(x)/g(x) = remainder of q(x)/g(x)
So, 27a + 41 = 15 + a
27a - a = 15 - 41
26a = -26
a = -1
Therefore, the value of a is -1.
✦ Try This: If the polynomials z³ + az² + az - 4 and z³ - 2z + a leave the same remainder when divided by z - 2, find the value of a.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 2
NCERT Exemplar Class 9 Maths Exercise 2.4 Problem 1
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
Summary:
If the polynomials az³ + 4z² + 3z - 4 and z³ - 4z + a leave the same remainder when divided by z - 3, the value of a is -1
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