Question
Which of the following quadratic equations is not solvable by grouping?
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(1 point)
Responses
x2−2x+1=0
x squared minus 2 x plus 1 is equal to 0
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
Desmos Calculator (click here)
(1 point)
Responses
x2−2x+1=0
x squared minus 2 x plus 1 is equal to 0
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
Answers
GPT-4o mini
To determine which quadratic equation is not solvable by grouping, we first need to understand what it means to solve a quadratic equation by grouping. This method typically involves rearranging a quadratic in a form that can be factored by grouping terms.
Let's analyze each equation:
1. **\(x^2 - 2x + 1 = 0\)**:
- This can be factored as \((x - 1)(x - 1) = 0\) or \( (x - 1)^2 = 0\). It can be solved by grouping.
2. **\(2x^2 + 14x + 12 = 0\)**:
- This can be factored as \(2(x^2 + 7x + 6) = 0\), which can be further factored as \(2(x + 6)(x + 1) = 0\). It is solvable by grouping.
3. **\(2x^2 - 2x - 10 = 0\)**:
- We can divide all terms by 2: \(x^2 - x - 5 = 0\). Factoring it directly is not straightforward, but it can be solved using the quadratic formula. Grouping is not an obvious method here.
4. **\(x^2 - 12x + 35 = 0\)**:
- This can be factored as \((x - 5)(x - 7) = 0\). It can be solved by grouping.
From this analysis, the equation **\(2x^2 - 2x - 10 = 0\)** is the one that is not easily solvable by grouping, as it does not lend itself to a clean factoring technique without further methods like the quadratic formula.
Let's analyze each equation:
1. **\(x^2 - 2x + 1 = 0\)**:
- This can be factored as \((x - 1)(x - 1) = 0\) or \( (x - 1)^2 = 0\). It can be solved by grouping.
2. **\(2x^2 + 14x + 12 = 0\)**:
- This can be factored as \(2(x^2 + 7x + 6) = 0\), which can be further factored as \(2(x + 6)(x + 1) = 0\). It is solvable by grouping.
3. **\(2x^2 - 2x - 10 = 0\)**:
- We can divide all terms by 2: \(x^2 - x - 5 = 0\). Factoring it directly is not straightforward, but it can be solved using the quadratic formula. Grouping is not an obvious method here.
4. **\(x^2 - 12x + 35 = 0\)**:
- This can be factored as \((x - 5)(x - 7) = 0\). It can be solved by grouping.
From this analysis, the equation **\(2x^2 - 2x - 10 = 0\)** is the one that is not easily solvable by grouping, as it does not lend itself to a clean factoring technique without further methods like the quadratic formula.