Question
5. Which of the following quadratic equations is not solvable by grouping?(1 point)
Responses
2x2+14x+12=0
2 x squared plus 14 x plus 12 is equal to 0
2x2−2x−10=0
2 x squared minus 2 x minus 10 is equal to 0
x2−12x+35=0
x squared minus 12 x plus 35 is equal to 0
x2−2x+1=0
Responses
2x2+14x+12=0
2 x squared plus 14 x plus 12 is equal to 0
2x2−2x−10=0
2 x squared minus 2 x minus 10 is equal to 0
x2−12x+35=0
x squared minus 12 x plus 35 is equal to 0
x2−2x+1=0
Answers
GPT-4o mini
To determine which quadratic equation is not solvable by grouping, we can look at the ability to factor each equation.
1. **2x² + 14x + 12 = 0**
This can be factored: Factor out a 2 first:
\(2(x^2 + 7x + 6) = 0\)
Then \(x^2 + 7x + 6\) can be factored into \((x + 1)(x + 6)\), so this is solvable by grouping.
2. **2x² − 2x − 10 = 0**
Factor out a 2:
\(2(x^2 - x - 5) = 0\)
The expression \(x^2 - x - 5\) does not factor nicely into rational numbers, thus it's not directly solvable by grouping.
3. **x² − 12x + 35 = 0**
This factors into \((x - 5)(x - 7) = 0\). So this is solvable by grouping.
4. **x² − 2x + 1 = 0**
This can be factored into \((x - 1)(x - 1) = (x - 1)^2 = 0\). So this is also solvable by grouping.
Based on this analysis, the equation that is not solvable by grouping is:
**2x² − 2x − 10 = 0**.
1. **2x² + 14x + 12 = 0**
This can be factored: Factor out a 2 first:
\(2(x^2 + 7x + 6) = 0\)
Then \(x^2 + 7x + 6\) can be factored into \((x + 1)(x + 6)\), so this is solvable by grouping.
2. **2x² − 2x − 10 = 0**
Factor out a 2:
\(2(x^2 - x - 5) = 0\)
The expression \(x^2 - x - 5\) does not factor nicely into rational numbers, thus it's not directly solvable by grouping.
3. **x² − 12x + 35 = 0**
This factors into \((x - 5)(x - 7) = 0\). So this is solvable by grouping.
4. **x² − 2x + 1 = 0**
This can be factored into \((x - 1)(x - 1) = (x - 1)^2 = 0\). So this is also solvable by grouping.
Based on this analysis, the equation that is not solvable by grouping is:
**2x² − 2x − 10 = 0**.