Finding b in a peculiar quadratic formula

Question

So, the equation is described as:

(x^2 -ax- 4) / (x + 1) = 0. The question states that there is one solution to the quadratic formula and is asking me to find the value of a (I wrote it as being b in the question as "a" in this question corresponds to the b in the quadratic formula)

I have tried multiplying both sides by x+1 and solve it from there, but I can't seem to be able to get the text book answer, which is a=3

Answer 1

Your question isn't entirely clear.

(x² - ax -4)/(x +1) will have only a single solution if x +1 is a factor of the numerator.

If (x + 1)(x - q) = x^x - ax -4

x² - (1-q)x - q must be identically equal to x² - ax -4, i.e. q = 4 and -a = -(1-q) => a = 3

As long as x not equal -1 then the factor will divide out and the equation will have the single root x = 4.