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
You're on a roll — Let's solve question 9 using the quadratic formula. The equation is 6m^2 - m - 2 = 0. Step 1: Identify the coefficients a, b, and c. Comparing 6m^2 - m - 2 = 0 with the standard quadratic form am^2 + bm + c = 0, we have: a = 6 b = -1 c = -2 Step 2: Apply the quadratic formula. The quadratic formula is m = -b ± sqrt(b^2 - 4ac)2a. Step 3: Substitute the values of a, b, and c into the formula. m = -(-1) ± sqrt((-1)^2 - 4(6)(-2))2(6) Step 4: Simplify the expression. m = 1 ± sqrt(1 - (-48))12 m = 1 ± sqrt(1 + 48)12 m = 1 ± sqrt(49)12 m = (1 ± 7)/(12) Step 5: Calculate the two possible solutions for m. For the positive root: m_1 = (1 + 7)/(12) = (8)/(12) = (2)/(3) For the negative root: m_2 = (1 - 7)/(12) = (-6)/(12) = -(1)/(2) The solutions are m = (2)/(3) and m = -(1)/(2). m = (2)/(3), -(1)/(2) What's next?