What value for c will make the expression a perfect square trinomial? x2 – 7x + c negative StartFraction 49 Over 4 EndFraction negative seven-halves seven-halves StartFraction 49 Over 4 EndFraction

Accepted Solution

Answer: [tex]c=\frac{49}{4}[/tex]Step-by-step explanation: You can find the value of "c" that will make it a perfect square trinomial by Completing the square. Given the following expression provided in the exercise: [tex]x^2 - 7x + c[/tex] You can notice that it is written in this form: [tex]ax^2-bx+c[/tex] Then, you can identify that the coefficient "b" is: Β [tex]b=-7[/tex] Since to complete the square you must add and subtract the half of square of coefficient "b", you can conclude that: [tex]c=(\frac{b}{2})^2[/tex] Therefore, substituting "b" into [tex]c=(\frac{b}{2})^2[/tex], you get: [tex]c=(\frac{-7}{2})^2\\\\c=\frac{49}{4}[/tex]