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 4…

Question

asked Jun 26, 2020 60.7k views

2 Answers

Eugene Alexeev · Answer 1 · 2020-06-30T19:35:01+0000

Answer:
c=(49)/(4)

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:

x^2 - 7x + c

You can notice that it is written in this form:

ax^2-bx+c

Then, you can identify that the coefficient "b" is:

b=-7

Since to complete the square you must add and subtract the half of square of coefficient "b", you can conclude that:

c=((b)/(2))^2

Therefore, substituting "b" into
c=((b)/(2))^2 , you get:

$c=((-7)/(2))^2\\\\c=(49)/(4)$