MCQ
If x3 - 3x2 + 3x - 7 = (x + 1)(ax2 + bx + c), then a + b + c =
- A4
- B12
- C-10
- D3
✓
Answer
- -10
Solution:
The given equation is
x3 - 3x2 + 3x - 7 = (x + 1)(ax2 + bx + c)
This can be written as
x3 - 3x2 + 3x - 7 = (x + 1)(ax2 + bx + c)
= x3 - 3x2 + 3x - 7 = ax3 + bx2 + cx + ax2 + bx + c
= x3 - 3x2 + 3x - 7 = ax3 + (a + b)x2 + (b + c)x + c
Comparing the cofficients on both sides of the equation.
We get,
a = 1 ...(1)
a + b = 3 ...(2)
b + c = 3 ...(3)
c = -7 ...(4)
Putting the value of a form (1) in (2)
We get,
1 + b = 3,
b = -3 - 1
b= -4
So the value of a, b and c is 1, -4 and -7 respectively.
Therefore,
a + b + c = 1 - 4 - 7 = -10
Hence, correct option is (c).
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