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sladkih [1.3K]
2 years ago
8

Which of the following constants can be added to x^2 + 2/3x to form a perfect square trinomial?

Mathematics
2 answers:
morpeh [17]2 years ago
6 0
Take 1/2 of the linear coefient and square it

2/3 times 1/2=1/3
square 1/3 to get 1/9

the constnat is 1/9
it would factor to (x+1/3)^2
LenaWriter [7]2 years ago
5 0

Answer:

\frac{1}{9}  is to be added to make x^2+\frac{2}{3}x  a perfect square trinomial as (x+\frac{1}{3})^{2}

Step-by-step explanation:

Given : x^2+\frac{2}{3}x  

We have to find what can be added to  x^2+\frac{2}{3}x to form a perfect square trinomial.

Perfect square trinomial is of the form (a+b)^2

Consider the given expression x^2+\frac{2}{3}x

Using algebraic identity (a+b)^2=a^2+b^2+2ab ,

Comparing , we get,  a = x ......(1)

2ab=\frac{2}{3}x

Uisng (1) , we get,

2b=\frac{2}{3} \\\\ \Rightarrow b=\frac{1}{3}

To make it  a perfect square trinomial we need to add b^2 term

b^2=\frac{1}{9}

Thus, \frac{1}{9}  is to be added to make x^2+\frac{2}{3}x  a perfect square trinomial as (x+\frac{1}{3})^{2}

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