Question

Select all of the following that are solutions to the equation x2+3x−10=0 . There may be more than one solution.(2 points) Responses 10 10 2 2 −5 negative 5 5

Answer 1

To find the solutions to the equation \( x^2 + 3x - 10 = 0 \), we can factor the quadratic equation, use the quadratic formula, or complete the square.

First, let's factor the equation. We are looking for two numbers that multiply to -10 (the constant term) and add to 3 (the coefficient of \( x \)).

The numbers that meet these criteria are 5 and -2. We can write:

\[
(x + 5)(x - 2) = 0
\]

Setting each factor equal to zero gives the solutions:

1. \( x + 5 = 0 \) → \( x = -5 \)
2. \( x - 2 = 0 \) → \( x = 2 \)

Thus, the solutions to the equation \( x^2 + 3x - 10 = 0 \) are \( x = -5 \) and \( x = 2 \).

From the responses provided:
- 10 (not a solution)
- 2 (solution)
- -5 (solution)
- 5 (not a solution)

The correct solutions are:

**2 and -5**.