The image shows the quadratic formula, $x = \frac{-b \pm \sqrt{D}}{2a}$, and the statement "If $D < 0$, 0 real solution". The problem is about the nature of solutions to a quadratic equation when the discriminant $D$ is negative. The expression $x = \frac{-b \pm \sqrt{D}}{2a}$ is the quadratic formula for finding the roots of a quadratic equation of the form $ax^2 + bx + c = 0$, where $D = b^2 - 4ac$ is the discriminant.

1. Problem Description

The image shows the quadratic formula, $x = \frac{-b \pm \sqrt{D}}{2a}$, and the statement "If $D < 0$, 0 real solution". The problem is about the nature of solutions to a quadratic equation when the discriminant $D$ is negative. The expression $x = \frac{-b \pm \sqrt{D}}{2a}$ is the quadratic formula for finding the roots of a quadratic equation of the form $ax^2 + bx + c = 0$, where $D = b^2 - 4ac$ is the discriminant.

2. Solution Steps

The quadratic formula is given by

$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

The discriminant is given by

$D = b^2 - 4ac$

The nature of the roots depends on the value of the discriminant $D$.

If $D > 0$, there are two distinct real roots.

If $D = 0$, there is one real root (a repeated root).

If $D < 0$, the square root of $D$ is an imaginary number, so there are two complex conjugate roots, and there are no real roots.

Therefore, if $D < 0$, there are zero real solutions.

3. Final Answer

If $D < 0$, the quadratic equation has no real solutions, only two complex solutions. The image states "0 real solution" which means no real solutions.