Find possible values of the constant p if the expression Px + 12x + 4p + px2 is a perfect square.

April 3, 2026Mathematics

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April 3, 2026

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Here are the solutions to the problems you provided:

1. Find possible values of the constant p if the expression $Px + 12x + 4p + px^2$ is a perfect square.

Assuming the capitalized 'P' is a typo and should be 'p', the expression is $px^2 + (p+12)x + 4p$ . For a quadratic expression $ax^2 + bx + c$ to be a perfect square, its discriminant must be zero ( $b^2 - 4ac = 0$ ). Here, $a = p$ , $b = p+12$ , and $c = 4p$ .

Step 1: Set the discriminant to zero.

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--- 1. Find possible values of the constant p if the expression Px + 12x + 4p + px^2 is a perfect square.

Asked on April 3, 2026Mathematics

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 AnswerAnswered on April 3, 2026

Here are the solutions to the problems you provided: --- 1. Find possible values of the constant p if the expression Px + 12x + 4p + px^2 is a perfect square. Assuming the capitalized 'P' is a typo and should be 'p', the expression is px^2 + (p+12)x + 4p. For a quadratic expression ax^2 + bx + c to be a perfect square, its discriminant must be zero (b^2 - 4ac = 0). Here, a = p, b = p+12, and c = 4p. Step 1: Set the discriminant to zero. (p+12)^