Question

Find the value of c that makes the trinomial a perfect square.


Find the value of c that makes x2 – 2x + c a perfect square trinomial.



a 1

b 2

c -1/2

d –4

Answer 1

Answer:

a. 1

Step-by-step explanation:

$(a-b)^2=a^2-2ab+b^2\\\\\text{We have}\ x^2-2x+c=x^2-2(x)(1)+c.\\\\\text{Therefore}\ c=1^2=1\\\\x^2-2(x)(1)+1^2=(x-1)^2$

Answer 2

Answer:

a

Step-by-step explanation:

Given

x² - 2x + c

is a perfect square of the form

(x - a)² = x² - 2ax + a² compare with x² - 2x + c, then

- 2a = - 2 ⇒ a = 1, thus

a² = 1² = 1 = c

(x - 1)² = x² - 2x + 1 ← perfect square trinomial