Answer:
c=9
Step-by-step explanation:
[tex]x^2+6x+c[/tex]
The given polynomial is a perfect square trinomial.
using completing square method to find the perfect square.
[tex]\Rightarrow x^2+6x+c[/tex]
[tex]a^2+2ab+b^2=(a+b)^2[/tex]
Now we compare the given polynomial
[tex]a^2+2ab+b^2\rightarrow x^2+2\cdot 3\cdot x+c[/tex]
[tex]a^2\rightarrow x^2[/tex]
[tex]2ab\rightarrow 2\cdot 3\cdot x[/tex]
[tex]b^2\rightarrow c[/tex]
2ab=6x
b=3
But [tex]b^2\rightarrow c[/tex]
So, c=9
Hence, The value of c is 9 to make perfect square.
