00:01
Given data is f of x equal to x squared minus 4x minus 27.
00:12
And f of c equal to 5.
00:18
Now we have to find out the values of c.
00:24
We can write f of c equal to here we will replace each occurrence of x with c.
00:32
So c square minus 4c minus 27 and we already know that f of c equal to 5.
00:42
So 5 is equal to c square minus 4c minus 27.
00:49
Now move all the terms to one side so that we will obtain 0 on other side.
00:57
C square minus 4c minus 27 minus 5 is equal.
01:04
To 0.
01:06
Now add like terms c squared minus 4c minus 32 is equal to 0.
01:16
To get the values of c we have to factor c squared minus 4c minus 32 equal to 0.
01:25
For that we will rewrite the middle term minus 4c as c square minus 8c plus 4c minus 3 2 is equal to 0.
01:38
Because we want two integers whose product is constant minus 32 and whose sum is equal to coefficient of middle term minus 4.
01:57
Here we took integers minus 8 and 4...