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
Here are the solutions to the questions: 1. Find possible values of the constant p if the expression Px^2 - 12x + 4p is a perfect square. For a quadratic expression Ax^2 + Bx + C to be a perfect square, its discriminant must be zero, i.e., B^2 - 4AC = 0. In this expression, A = P, B = -12, and C = 4p. Step 1: Set the discriminant to zero. (-12)^2 - 4(P)(4p) = 0 Step 2: Simplify the equation. 144 - 16P^2