Answer
$p = 3$ or $p = 1$
Work Step by Step
We are asked to solve this quadratic equation using the Quadratic Formula, which is given as:
$x = \dfrac{-b ± \sqrt {b^2 - 4ac}}{2a}$, where $a$ is the coefficient of the squared term, $b$ is the coefficient of the linear term, and $c$ is the constant term.
In this exercise, $a = 1$, $b = -4$, and $c = 3$.
Plug these values into the Quadratic Formula, replacing $x$ with $p$:
$p = \dfrac{-(-4) ± \sqrt {(-4)^2 - 4(1)(3)}}{2(1)}$
$p = \dfrac{-(-4) ± \sqrt {16 - 4(1)(3)}}{2(1)}$
$p = \dfrac{4 ± \sqrt {16 - 12}}{2}$
$p = \dfrac{4 ± \sqrt {4}}{2}$
$p = \dfrac{4 ± 2}{2}$
Perform the operations within the numerator:
$p = \frac{6}{2}$ or $p = \frac{2}{2}$
Simplify the fraction:
$p = 3$ or $p = 1$
