For integers \(b\) and \(c\), what is the sum of all unique

[VJesus12]

For integers \(b\) and \(c\), what is the sum of all unique solutions to the equation \(x^2−bx+c=10x^2−bx+c=10?\)

(1) \(c = 59\)
(2) \(b = 14\)

[spoiler]OA=C[/spoiler]

Source: Veritas Prep

[deloitte247]

$$x^2-bx+c=10$$
$$x^2-bx+\left(c-10\right)=0$$
Sum of the roots of a quadractic equation = -b/a
Where b=b, and a=1
Sum = -b/1
Question=> What is the sum of all unique solutions?
Sum of roots = -b/a
Product of roots = c/a
We are looking for the sum of roots that provides a solution to the quadratic equation and answers -b/a.
Statement 1: c = 59
Remember that the solution of a quadratic equation is called its roots.
Therefore, sum of roots = -b/a, where a=1, b=?
Since'b' is not known, statement 1 is NOT SUFFICIENT.

Statement 2: b=14
Sum or roots = -14/1 = -14
Statement 2 alone is SUFFICIENT.

Answer is option B.