If 2x cube+ 3x2 + ax + b is divided by (x - 2) leaves the remainder 2 and divided by (x + 2) leaves the
remainder-2, then the values of a, b are respectively
[ ]
a) 7,12
b) -7,12
c) 7,-12
d) -7, -12
TE
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If 2x cube+ 3x2 + ax + b is divided by (x - 2) leaves the remainder 2 and divided by (x + 2) leaves the
remainder-2, then the values of a, b are respectively
[ ]
a) 7,12
b) -7,12
c) 7,-12
d) -7, -12
TE
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Verified answer
ANSWER:
GIVEN:
TO FIND:
EXPLANATION:
x - 2 = 0
x = 2
When 2x³ + 3x² + ax + b is divided by (x - 2), it leaves the remainder 2.
2(2)³ + 3(2)² + a(2) + b = 2
2(8) + 3(4) + 2a + b = 2
16 + 12 + 2a + b = 2
28 + 2a + b = 2
2a + b = - 26 -----> 1
x + 2 = 0
x = - 2
When 2x³ + 3x² + ax + b is divided by (x + 2), it leaves the remainder - 2.
2(- 2)³ + 3(- 2)² + a( - 2) + b = - 2
2(-8) + 3(4) - 2a + b = - 2
-16 + 12 - 2a + b = - 2
- 4 - 2a + b = - 2
- 2a + b = 2 -----> 2
Add equations 1 and 2
2a + b - 2a + b = - 26 + 2
2b = - 24
b = - 12
Substitute b = - 12 in equation 1.
2a - 12 = - 26
2a = - 14
a = - 7
Hence the value of a = - 7 and b = - 12.
VERIFICATION:
16 + 12 + 2a + b = 2
Substitute a = -7 and b = - 12
16 + 12 + 2( - 7) - 12 = 2
16 + 12 + - 14 - 12 = 2
16 - 14 = 2
2 = 2
-16 + 12 - 2a + b = - 2
Substitute a = -7 and b = - 12
-16 + 12 - 2(- 7) - 12 = - 2
-16 + 12 + 14 - 12 = - 2
- 16 + 14 = - 2
-2 = - 2
HENCE VERIFIED.
Answer:
-7,-12
Step-by-step explanation:
Substitute b = - 12 in equation 1.