Question

What number must be added to each binomial to make a perfect square trinomial?


x^2-5x+?

Answer 1

(-5/2)^2

Answer 2

\[ add~\left( half~ the~ co-efficient~ of ~x \right)^2\]

Answer 3

(-5x/2)^2

Answer 4

ok so would it be 25/4 ?

Answer 5

\(\begin{array}{cccccllllll}
{\color{brown}{ a}}^2& + &2{\color{brown}{ a}}{\color{blue}{ b}}&+&{\color{blue}{ b}}^2\\
\downarrow && &&\downarrow \\
{\color{brown}{ a}}&& &&{\color{blue}{ b}}\\
&\to &({\color{brown}{ a}} + {\color{blue}{ b}})^2&\leftarrow
\end{array}\qquad

% perfect square trinomial, negative middle term
\begin{array}{cccccllllll}
{\color{brown}{ a}}^2& - &2{\color{brown}{ a}}{\color{blue}{ b}}&+&{\color{blue}{ b}}^2\\
\downarrow && &&\downarrow \\
{\color{brown}{ a}}&& &&{\color{blue}{ b}}\\
&\to &({\color{brown}{ a}} - {\color{blue}{ b}})^2&\leftarrow
\end{array}\)

notice, the middle term is
2 * term on left * term on right

so the terms without the exponent
so 2 * x * "something" = 5x <----- so solve for "something"

Answer 6

oh so its 2*1*x=5
so x= 5/2

Answer 7

25/4 is correct