SOLUTION: Find b if f(x)= x^2-bx+9 has one rational root and b >0.

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Question 1118792: Find b if f(x)= x^2-bx+9 has one rational root and b >0.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
highlight%28b=6%29


One root, then f is perfect square
x%5E2-6x%2B9=%28x-3%29%5E2
and the one root is 3.

Answer by ikleyn(52855) About Me  (Show Source):
You can put this solution on YOUR website!
.
f(x) = x^2 - bx + 9.


f(x) has one rational root if and only if the discriminant of this quadratic equation is zero


d = (-b)^2 - 4*1*9 = 0,   or   b^2 - 36 = 0,


which implies  b = +/-6.


Since the problem requires  b > 0,  there is only one solution  b = 6.