Math CentralQuandaries & Queries


Question from Kevin, a teacher:

Find a value of n such that f(x) = 3^x2 + nx + 6 only has one zero, is this the only solution to the question?

Hi Kevin,

The key hear is the general quadratic. If $ax^2 + bx + c = 0$ then x is given by

\[x = \frac{-b \pm \sqrt{b^2 - 4 a c}}{2a}.\]

If $b^2 - 4 ac >0$ then the square root gives you two solutions, one with the plus sign and the other with the minus sign.

If $b^2 - 4 ac <0$ then the square root does not yield a real number and hence there are no real solution.

If $b^2 - 4 ab = 0$ then there is one solution.


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