Question

Find the value of c that makes z2 - 5z + c a perfect square trinomial.

C= *BLANK*

Write the expression as the square of a binomial.
The expression is *BLANK*

Answer 1

• z²-5z+c=0
• z²-2(z)(2.5)+c=0

Add and subtract 2.5²

• z²-2(z)(2.5)+2.5²-2.5²+c=0
• (z-2.5)²-6.25+c=0

So

• c-6.25=0
• c=6.25

Answer 2

• c = 6.25

Explanation:

Given trinomial:

• z² - 5z + c

Complete square:

• z² - 2*2.5*z + 2.5² + c - 2.5² =
• (x - 2.5)² + c - 6.25

The value of c:

• c - 6.25 = 0
• c = 6.25