For which value of $c$ does the quadratic equation

$5x^2 - 6x + c = 0$

have exactly one solution in terms of $x$?

The solution is supposed to be $c = 1.8$, but I only ever get $c = 1$

I've tried to solve this like:

$ax^2 + bx + c = 0\implies 5 - 6 + c = 0$

but since this does not match with the textbook solution, I think I'm operating from a false premise.

What am I doing wrong?

  • $\begingroup$ Exactly one solution does not mean that $x=1$ is a solution but that the number of solutions is $1$. $\endgroup$ – Did May 27 '12 at 11:11
  • $\begingroup$ Yes, I realized as much. $\endgroup$ – Miroslav Cetojevic May 27 '12 at 11:12

"Exactly one solution" means that there is only one value of $x$ that will solve the equation. It does not mean "has $1$ as an exact solution".

So what you want to do is figure out under what conditions the two roots of the quadratic will coincide. This occurs precisely when the discriminant of the quadratic, $b^2-4ac$, is equal to zero. You have $a=5$ and $b=-6$, which will let you solve for $c$.


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