The quadratic equation 2x^2 + bx + 18 = x^2 + 6x + 4 has a double root. Find all possible values of b.
+66 We can simplify first:
x^2 + (b - 6)x + 14 = 0
Now we can use a bit of brute force here:
(x + p)(x + q)
pq = 14
p + q = b - 6
(p, q) = (14, 1) (7, 2) (-14, -1) (-7, -2)
So we can plug the values of p and q in to get all the possible values of b:
14 + 1 = b - 6 --> b = 21
7 + 2 = b - 6 --> b = 15
-14 + -1 = b - 6 --> b = -9
-7 + -2 = b - 6 --> b = -3
Thus, all the possible values of b are: 21, 15, -9, -3.
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ShockFish
