To determine which of the given quadratic equations is not solvable by grouping, we typically look for a method of factoring that would be needed to solve the equation.
-
6x² + 37x + 6 = 0: This equation can be factored, and it would likely require grouping or trial and error.
-
x² + x - 90 = 0: This can be factored using integers that multiply to -90 and add to +1. It can be solved by grouping.
-
x² - 10x + 9 = 0: This can also be factored directly as (x - 9)(x - 1) = 0.
-
3x² - 9x + 4 = 0: This is less straightforward to factor. To solve it, one might consider using the quadratic formula since it doesn't neatly factor into products of linear terms.
Out of these equations, 3x² - 9x + 4 = 0 is the one that is typically not solvable by grouping due to the nature of its coefficients and would usually require the quadratic formula or completing the square.
So, the answer is 3x² - 9x + 4 = 0.
1 answer