Joana solved the equation 4x ^ 2 - 4x - 3 = 0 She followed the steps to solve a quadratic equation by grouping. However, in Step 3 she noticed that the two groupings did not share a common binomial, as shown in her work below. She concluded that the quadratic equation 4x ^ 2 - 4x - 3 = 0 has no solutionsIs Joana's conclusion correct ? Review Joana's work to answer the question Step 1: 4x ^ 2 + 2x + (- 6x) - 3 = 0 Step 2: (4x ^ 2 + 2x) + (- 6x - 3) = 0 Step 3: x(4x + 2) + (- 3(2x + 1)) = 0 ( 1 point) Yes, because the two groupings do not share a common binomial Yes, because there are no factors of -12 that add up to -4 No, because she can still continue the steps even if the two groupings have no shared binomial No, because she did not factor out the GCF from the first grouping
Joana's conclusion is incorrect. The presence of a common binomial is not necessary for solving a quadratic equation by grouping. She can still continue with the steps even if the two groupings do not share a common binomial. The correct answer would be: No, because she can still continue the steps even if the two groupings have no shared binomial.
