For what value of k, the function 3x³ + 9x² – (3k – 4)x + 2 is completely divisible by x - 1?
- 6
- 4
- 2
- None of these
Explanation
To find the value of k, use the Factor Theorem:
If a polynomial f(x) is completely divisible by (x - a), then f(a) = 0.
In this case, the polynomial is:
f(x) = 3x³ + 9x² - (3k - 4)x + 2
Since it's divisible by (x - 1), substitute x = 1:
f(1) = 3(1)³ + 9(1)² - (3k - 4)(1) + 2
= 3 + 9 - 3k + 4 + 2
= 18 - 3k
Set f(1) = 0:
18 - 3k = 0
Solve for k:
3k = 18
k = 6
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- 3
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- None of these
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اس سوال کو وضاحت کے ساتھ پڑھیں
