Which of the following quadratic equations is not solvable by grouping? (1 point)
022=2+1=0
022-122+35=0
0 222 - 22 - 10 = 0
022+14¢+12=0
The quadratic equation that is not solvable by grouping is:
0 222 - 22 - 10 = 0
To determine which quadratic equation is not solvable by grouping, let's first understand what grouping means in this context. Grouping refers to rearranging the terms of a quadratic equation in order to factor it.
Let's analyze each equation to see if grouping can be applied:
1) 022=2+1=0
This equation seems to be incomplete or incorrectly written. The terms are not quadratic, and there is an equal sign in the middle. Therefore, it cannot be solved by grouping.
2) 022-122+35=0
To apply grouping to this equation, we first need to rearrange the terms:
(0 222) - (22) - (10) = 0
Now, we can group the terms:
[(0 222) - (22)] - (10) = 0
It is solvable by grouping.
3) 0 222 - 22 - 10 = 0
This equation is similar to the previous one. By rearranging the terms and applying grouping, it can also be solved.
4) 022+14¢+12=0
Again, this equation seems to be incompletely written, and it is difficult to understand what "14¢" represents. Therefore, it cannot be solved by grouping.
Therefore, the quadratic equation not solvable by grouping is:
022+14¢+12=0.
To determine which of the quadratic equations is not solvable by grouping, we need to look at each equation and check if it can be factored using grouping.
1. 022 = 2 + 1 = 0: This equation cannot be solved using grouping because it is not a quadratic equation. The equation is linear, and there is no quadratic term.
2. 022 - 122 + 35 = 0: To factor this equation by grouping, we need to identify two pairs of terms that have a common factor. However, this equation cannot be factored using grouping because the terms do not have any common factors. Therefore, it is not solvable by grouping.
3. 0 222 - 22 - 10 = 0: This equation can be solved using grouping. We can group the middle terms: (0 222 - 22) - 10 = 0. From here, we can factor out the common factor (2) in the first group: 2(0111 - 11) - 10 = 0. Simplifying further, we get 2(0110) - 10 = 0. Thus, this equation is solvable by grouping.
4. 022 + 14¢ + 12 = 0: This equation cannot be solved using grouping because it is not in standard quadratic form. The equation appears to have some typographical errors, such as "14¢" which is not clear. Without the correct formulation, we cannot determine if it can be factored using grouping.
In conclusion, the quadratic equation that is not solvable by grouping is option 2: 022 - 122 + 35 = 0.