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If (x + 1) is factor of \( \Large 2x^{3} - ax^{2} - (2a - 3) x + 2 \), then the value of 'a' is
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A) 3 |
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B) 2 |
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C) \( \Large \frac{3}{2} \) |
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D) \( \Large \frac{1}{2} \) |
Correct Answer:
| A) 3 |
Description for Correct answer:
Let \( \Large \int{(x)} = 2x^{3} - ax^{2} - (2a - 3)x + 2 = 0 \)
If (x + 1) is a factor of the above expression, then \( \Large \int{(-1)} = 0 \)
\( \Large \therefore \int{-1} = 2(-1)^{3} - a(-1)^{2} - (2a - 3) \times -1 + 2 = 0 \)
=> - 2 - a + 2a - 3 + 2 = 0
=> a - 3 = 0
=> a = 3
Let \( \Large \int{(x)} = 2x^{3} - ax^{2} - (2a - 3)x + 2 = 0 \)
If (x + 1) is a factor of the above expression, then \( \Large \int{(-1)} = 0 \)
\( \Large \therefore \int{-1} = 2(-1)^{3} - a(-1)^{2} - (2a - 3) \times -1 + 2 = 0 \)
=> - 2 - a + 2a - 3 + 2 = 0
=> a - 3 = 0
=> a = 3
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