When a polynomial 2x(square)+3x(square)+ax+b is divided by (x-2) leaves remainder 2 & divided by (x+2) leaves remainder -2. Find a&b
Answers
Value of a is -7 and Value of b is -12
Step-by-step explanation:
Given polynomial:
p(x) = 2x³ + 3x² + ax + b
when p(x) is divided by x - 2 leaves remainder = 2
when p(x) is divided by x + 2 leaves remainder = -2
To find: Value of a and b
We use remainder theorem.
Remainder Theorem states that if a polynomial p(x) is divided by a polynomial of form x - a then the remainder = p(a).
So,
when p(x) is divided by x - 2 ,
Remainder = p(2)
2(2)³ + 3(2)² + a(2) + b = 2
16 + 12 + 2a + b = 2
2a + b = 2 - 28
2a + b = -26 ...............................(1)
when p(x) is divided by x + 2 ,
Remainder = p(2)
2(-2)³ + 3(-2)² + a(-2) + b = -2
-16 + 12 - 2a + b = -2
-2a + b = -2 + 4
-2a + b = 2 ...............................(2)
Add (1) and (2)
b + b = -26 + 2
2b = -24
b = -12
Put value of b in (1)
2a + (-12) = -26
2a = -26 + 12
2a = -14
a = -7
Therefore, Value of a is -7 and Value of b is -12
Answer:
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