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 — Step 1: Understand the definition of a zero of a polynomial. If x=a is a zero of a polynomial f(x), it means that when x=a is substituted into the polynomial, the result is 0, i.e., f(a) = 0. Step 2: Substitute the given zero into the polynomial. Given the polynomial f(x) = x^2 + px + 12 and one of its zeros is x=4. Therefore, we set f(4) = 0. Step 3: Set up the equation and solve for p. Substitute x=4 into the polynomial: (4)^2 + p(4) + 12 = 0 16 + 4p + 12 = 0 4p + 28 = 0 Subtract 28 from both sides: 4p = -28 Divide by 4: p = (-28)/(4) p = -7 The value of the constant p is -7. Send me the next one 📸