Answer
The statement is false.
To make it true, replace "Every..." with "Not every ...".
Work Step by Step
In the quadratic formula, $ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$
we have a radicand, $ b^{2}-4ac $, which may be positive, zero, or negative.
The number of real solutions depends on its value, because a square root is taken from it.
The expression is called the discriminant, and when it is
- positive, there will be two distinct real solutions to the quadratic equation,
- zero, there will be ONE real solution (double real zero)
- negative, there will be no real solutions (the two solutions are complex conjugates)
So, not every quadratic equation has 2 distinct solutions.
The statement is false.
To make it true, replace "Every..." with "Not every ...".
