Question

Hi!

I'm having trouble with the following question:

"Solve the following quadratic formula by completing the square:

x^2 -2x +a = 0 "

So far, I'm managed to find out that

a)The equation has 2 distinct roots because
"b^2 -4ac" = positive

b) One of the roots is 1.

My textbook says that the other answer is sqrt(1-a) but I can't get that answer. My calculations show that the answer should be (sqrt(1-a) + 1 )

Could you please show working? Thanks in advance!

Answer 1

so you know how to solve quadratics using completing the square method...
can you just post first few steps of your working??

Answer 2

i believe you reached till
\(\large x^2 -2x+1 = 1-a\)

right ??

Answer 3

oh and just so you know,
your answer of
\(\large x = \sqrt{1-a}+ 1 \)
is correct.
and the book is wrong

Answer 4

another answer is
\(\large x = -\sqrt{1-a} +1 \)

Answer 5

I did indeed reach \[x^{2}-2x +1 = 1-a\]

at which point it seemed that \[x-1 = \sqrt{1-a}\]

--

Glad to know that my answer was right though! I was ripping my hair out. Thanks for clarifying. c:

Answer 6

welcome ^_^

i see you're new here,
\(\Huge \mathcal{\text{Welcome To OpenStudy}\ddot\smile} \)

Answer 7

Haha, thank you for warm welcome! I'll probably be lurking around in these forums quite often. c: