Question
Which statement correctly interprets the solution(s) to the equation x2+5x+6=−3x2−2x
?(1 point)
Responses
There are no input values that would yield the same output value on both sides of the equation.
There are no input values that would yield the same output value on both sides of the equation.
An input of −3
will yield an output of 0 on both sides of the equation.
An input of negative 3 will yield an output of 0 on both sides of the equation.
An input of −2
will yield an output of 0 on both sides of the equation.
An input of negative 2 will yield an output of 0 on both sides of the equation.
An input of 0 will yield an output of 0 on both sides of the equation.
?(1 point)
Responses
There are no input values that would yield the same output value on both sides of the equation.
There are no input values that would yield the same output value on both sides of the equation.
An input of −3
will yield an output of 0 on both sides of the equation.
An input of negative 3 will yield an output of 0 on both sides of the equation.
An input of −2
will yield an output of 0 on both sides of the equation.
An input of negative 2 will yield an output of 0 on both sides of the equation.
An input of 0 will yield an output of 0 on both sides of the equation.
Answers
Answered by
GPT-4o mini
To interpret the solutions to the equation \( x^2 + 5x + 6 = -3x^2 - 2x \), we first need to simplify and solve the equation.
1. Combine all terms on one side:
\[
x^2 + 5x + 6 + 3x^2 + 2x = 0
\]
This gives:
\[
4x^2 + 7x + 6 = 0
\]
2. Now we can apply the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) where \( a = 4 \), \( b = 7 \), and \( c = 6 \).
3. Calculate the discriminant:
\[
b^2 - 4ac = 7^2 - 4(4)(6) = 49 - 96 = -47
\]
Since the discriminant is negative, there are no real solutions to the equation. This means there are no input values that yield the same output on both sides of the equation.
The correct interpretation of the solution is:
"There are no input values that would yield the same output value on both sides of the equation."
1. Combine all terms on one side:
\[
x^2 + 5x + 6 + 3x^2 + 2x = 0
\]
This gives:
\[
4x^2 + 7x + 6 = 0
\]
2. Now we can apply the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) where \( a = 4 \), \( b = 7 \), and \( c = 6 \).
3. Calculate the discriminant:
\[
b^2 - 4ac = 7^2 - 4(4)(6) = 49 - 96 = -47
\]
Since the discriminant is negative, there are no real solutions to the equation. This means there are no input values that yield the same output on both sides of the equation.
The correct interpretation of the solution is:
"There are no input values that would yield the same output value on both sides of the equation."