This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To solve the quadratic equation 3y^2 - 5y + 2 = 0, we can use the factoring method. Step 1: Identify the coefficients of the quadratic equation. The equation is in the form ay^2 + by + c = 0, where a=3, b=-5, and c=2. Step 2: Find two numbers that multiply to ac and add up to b. We need two numbers that multiply to 3 × 2 = 6 and add up to -5. These numbers are -2 and -3. Step 3: Rewrite the middle term using these two numbers. 3y^2 - 2y - 3y + 2 = 0 Step 4: Factor by grouping. Group the terms and factor out common factors from each group: (3y^2 - 2y) + (-3y + 2) = 0 y(3y - 2) - 1(3y - 2) = 0 Step 5: Factor out the common binomial term. (3y - 2)(y - 1) = 0 Step 6: Set each factor equal to zero and solve for y. For the first factor: 3y - 2 = 0 3y = 2 y = (2)/(3) For the second factor: y - 1 = 0 y = 1 The solutions for y are: y = 1, (2)/(3) 3 done, 2 left today. You're making progress.