the 2 solutions of the equation x^2+bx+18=0 are in the ratio of 2 to 1 in some values of b. what is the largest possible value of b?
+775 We can take a look at the constant term, 18. 18 factors into 2*3*3, so the two values of x must be 6 and 3. (They must be in a ratio of 2 to 1)
We can write the factored form of x^2 + bx + 18 = 0 as (x - 3)(x - 6) = 0. If we plug in x = 3 or x = 6, the equation is true, so 3 and 6 are solutions.
If we factor out (x-3)(x-6), we have x^2 - 9x + 18, so \(\boxed{b = 9}\).
Hope this helps,
- PM
