Question

If Q.No. 14, c =

पर्याय

•  b

• 2b

• 2b²

• −2b

Answer 1

We have to find the value of c

Given  `f(x)= ax^3 +bx -c` is divisible by the polynomial `g (x )= x^2 + bx + c`

We must have

`bx - acx +ab^2x + abc -c = 0 ` for all x

` x (b - ac + ab^2) + c (ab-1)= 0..........(1)`

`c (ab-1)=0`

Since  `c ` ≠ `0`, so

`ab - 1 = 0`

`ab = 1`

Now in the equation (1) the condition is true for all x. So put x = 1 and also we have ab = 1

Therefore we have

`b - ac + ab^2 = 0`

`b +ab^2 -ac =0`

`b(a +ab)-ac = 0`

Substituting `a= 1/b`and  `ab =1` we get,

`b(1 + 1) - 1/b xxc = 0`

`2b -1/b xxc =0`

`- 1/b xxc = -2b`

`cancel(-)1/bxx cancel(-) 2b`

` c = 2b =b/1`

`c = 2b ^2`

Hence, the correct alternative is `(c)`