Question

find the value of c such that each expression is a perfect square trinomial

Answer 1

2. The given expression is;

$z^2+2z+c$

We want to make the expression a perfect square trinomial.

In other words, we want to "complete the square".

In order to complete the square, we need to make c to be equal to

the square of the coefficient of the first power term divided by twice the coefficient of the first power term.

In other words,

$c=(\frac{b}{2a})^2$

Here, b =2 and a =1, so;

$c=(\frac{2}{2\times1})^2=1$

Therefore, the value of c to be added to make the expression a perfect square is 1

4. We have to find c;

$p^2-11p+c$

We know that; a = 1 and b = -11 , so ;

$\begin{gathered} c=(\frac{b}{2a})^2=(\frac{-11}{2})^2 \\ c=30.25 \end{gathered}$

Therefore, the value of c to be added to make the expression a perfect square is 30.25