+826 The roots of Ax^2+Bx+1 are the same as the roots of (x - 2)(x + 2). What is A+B?
+1926 First, let's focus on the expression we need A and B to be equal to.
In order to find what we need, we need to be able to compare coefficients. let's convert it to standard form.
We have
\((x - 2)(x + 2)=x^2-4\)
However, the constans don't match. Thus, we need to divide what we have by -4 to get a constant of +1.
We have
\(-\frac{1}{4}x^2+1\)
Now. we cam compare coefficients. Since A is the coefficient of x^2, we have
\(A=\frac{-1}{4}\)
Since B is the coefficient of x, we have \(B=0\)
Thus, we finally have \(A+B=-\frac{1}{4}+0 = -\frac{1}{4}\)
So -1/4 is our final answer.
Thanks! :)
