Solve the Quadratic Equation: x² + 5x + 10 = 0

$x^2+5x+10=0$

To solve this problem, we'll follow these steps:

• Step 1: Calculate the discriminant of the quadratic equation.
• Step 2: Use the discriminant to determine the number and type of solutions.

Step 1: Calculate the discriminant using the formula:

$\Delta = b^2 - 4ac = 5^2 - 4 \times 1 \times 10 = 25 - 40 = -15$.

Step 2: Analyze the discriminant:

• Since the discriminant ($\Delta$) is negative ($-15$), this indicates that the quadratic equation has no real solutions.

Therefore, the final solution is that the equation $x^2 + 5x + 10 = 0$ has no solution.

Comparing this with the given answer choices, the correct choice is:

Choice 3: No solution