Answer:
[tex]p = \frac{25}{4}[/tex]
Step-by-step explanation:
Given
[tex]x\² - 5x + p[/tex]
Required
Find p, such that the expression is a perfect square
Write out the coefficient of x
Coefficient = -5
Next step is to divide the coefficient of x by 2
[tex]Result = \½(-5)[/tex]
Take the square of the above expression to give p
[tex]p = (\½(-5))\²[/tex]
[tex]p = (\½(-5) * (\½(-5)[/tex]
[tex]p = \½ * \½ * (-5) * (-5)[/tex]
[tex]p = \¼(25)[/tex]
[tex]p = \frac{25}{4}[/tex]
Substitute 25/4 for p in the given expression
[tex]x\² - 5x + p[/tex] becomes
[tex]x\² -5x + \frac{25}{4}[/tex]
Expand the above expression
[tex]x\² - \frac{5x}{2} - \frac{5x}{2} + \frac{25}{4}[/tex]
Factorize
[tex]x(x - \frac{5}{2}) - \frac{5}{2}(x - \frac{5}{2})[/tex]
[tex](x - \frac{5}{2})(x - \frac{5}{2})[/tex]
[tex](x - \frac{5}{2})\²[/tex]
Hence, the value of p is [tex]p = \frac{25}{4}[/tex]
