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Question
If the polynomial f(x) = ax3 + bx − c is divisible by the polynomial g(x) = x2 + bx + c, then ab =
Options
1
- \[\frac{1}{c}\]
−1
- \[- \frac{1}{c}\]
Solution
We have to find the value of ab
Given f(x) = ax3 + bx − c is divisible by the polynomial g(x) = x2 + bx + c
We must have
`bx - acx + ab^2x + abc -c = 0 , for all x `
So put x = 0 in this equation
`x (b - ac +ab^2) + c (ab -1)= 0`
`c (ab -1)=0`
Since `c ≠ 0`, so
`ab -1 = 0`
`⇒ ab = 1`
Hence, the correct alternative is `(a)`.
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