Question

which of the following quadratic equations is NOT solvable by grouping

2x^2 - 2x - 10 = 0

x^2 - 12x + 35 = 0

2x^2 + 14x + 12 = 0

x^2 - 2x + 1 = 0

Answer 1

[AI-generated answer — Bot GPT 3.5]

The quadratic equation that is NOT solvable by grouping is x^2 - 2x + 1 = 0.

Answer 2

[AI-generated answer — Step-by-Step Bot]

To determine which quadratic equation is not solvable by grouping, we need to consider if the equation can be factored using the grouping method.

The grouping method involves splitting the middle term of the quadratic equation and finding common factors between the terms in each group.

Let's solve each quadratic equation using the grouping method:

1. 2x^2 - 2x - 10 = 0
The quadratic equation can be factored as follows:
2x^2 - 2x - 10 = 0
(2x + 4)(x - 5) = 0
Therefore, this equation is solvable by grouping.

2. x^2 - 12x + 35 = 0
The quadratic equation can also be factored using the grouping method:
x^2 - 12x + 35 = 0
(x - 7)(x - 5) = 0
Hence, this equation is solvable by grouping.

3. 2x^2 + 14x + 12 = 0
To determine if this equation can be factored by grouping, we need to find two numbers that multiply to give 2 * 12 = 24 (product) and add to give 14 (sum of the middle term). However, no such numbers exist. Therefore, this equation is not solvable by grouping.

4. x^2 - 2x + 1 = 0
This equation can be factored as follows:
x^2 - 2x + 1 = 0
(x - 1)(x - 1) = 0
This equation is solvable by grouping.

In conclusion, the quadratic equation that is NOT solvable by grouping is 2x^2 + 14x + 12 = 0.

Answer 3

[AI-generated answer — Explain Bot]

To determine which of the quadratic equations is NOT solvable by grouping, we need to understand what it means to solve a quadratic equation by grouping.

Solving a quadratic equation by grouping involves factoring the quadratic expression into two binomial terms. The goal is to rewrite the quadratic equation in the form (ax + b)(cx + d) = 0, where a, b, c, and d are constants. By setting each binomial factor equal to zero, we can solve for x.

Let's analyze each equation to determine if it can be solved using the grouping method:

1. 2x^2 - 2x - 10 = 0:
To solve this equation by grouping, we look for a common factor among the terms: 2x^2, -2x, and -10. Notice that we can factor out a 2 from all three terms:
2(x^2 - x - 5) = 0
Since (x^2 - x - 5) cannot be further factored, we cannot solve this equation by grouping.

2. x^2 - 12x + 35 = 0:
To solve this equation by grouping, we again look for a common factor among the terms. In this case, there is no common factor, so we cannot factor the expression by grouping:
x^2 - 12x + 35 = 0
Since we cannot factor the quadratic expression, we cannot solve this equation by grouping.

3. 2x^2 + 14x + 12 = 0:
To solve this equation by grouping, we check for a common factor. This equation can be factored by grouping using a common factor of 2:
2(x^2 + 7x + 6) = 0
The quadratic expression (x^2 + 7x + 6) can be further factored as (x + 6)(x + 1) = 0, so we can solve this equation by grouping.

4. x^2 - 2x + 1 = 0:
Similar to the previous equation, this quadratic equation can be factored using grouping. In this case, we factor out a common factor of 1:
(x - 1)(x - 1) = (x - 1)^2 = 0
Therefore, we can solve this equation by grouping.

From the analysis above, we can see that the quadratic equation that is NOT solvable by grouping is: x^2 - 12x + 35 = 0.