If 2x³ + ax² + BC - 6 has (x-1) as a factor and leaves a reminder 2 when divided by (x-2), find the value of a & b
A) a= -8 and b = 12
B) a=8 and b= -12
C) a= -4 and b= 10
D) a= 4 and b = -10
Please give a proper solution and ans it fast
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Answers
Answered by
11
see attachment....option(A) is correct
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Answered by
7
Hey friend,
option A) a= -8 b= 12 is the right answer.
f(x) = 2x³ + ax² + bx - 6
put x = 1
0 [since it is a factor of f(x) ] = 2(1)³ + a(1)² + b(1) -6
0 = 2 + a + b -6
a + b = 4 ------------------ eqn 1
f(x) = 2x³ + ax² + bx - 6
put x = 2
2 [ given remainder ] = 2(2)³ + a(2)² + b(2) -6
2 = 16 + 4a + 2b -6
2 = 4a + 2b + 10
4a + 2b = -8
2a + b = -4 --------------------------- eqn 2
on equating eqn 1& 2
a = -8
substitute the value of a in any eqn
b = 12.
Hope it helps...........................
option A) a= -8 b= 12 is the right answer.
f(x) = 2x³ + ax² + bx - 6
put x = 1
0 [since it is a factor of f(x) ] = 2(1)³ + a(1)² + b(1) -6
0 = 2 + a + b -6
a + b = 4 ------------------ eqn 1
f(x) = 2x³ + ax² + bx - 6
put x = 2
2 [ given remainder ] = 2(2)³ + a(2)² + b(2) -6
2 = 16 + 4a + 2b -6
2 = 4a + 2b + 10
4a + 2b = -8
2a + b = -4 --------------------------- eqn 2
on equating eqn 1& 2
a = -8
substitute the value of a in any eqn
b = 12.
Hope it helps...........................
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