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

• \[- \frac{1}{c}\]

Answer 1

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)`.