Question

what value of c makes the polynomial below perfect square?
4x^2+12x+c

Answer 1

nope

Answer 2

+4x%5E2 is the square of 2x

Answer 3

make the co-efficient as 1
\[4x ^{2}+12x+c=4\left( x ^{2}+3x \right)+c\]
\[ add \left( \frac{ co-efficient of x }{2 } \right)^{2}\]
\[=4\left( x ^{2} +3x+\left( \frac{ 3 }{ 2 } \right)^{2}-\left( \frac{ 3 }{ 2 } \right)^{2 } \right)+c\]
\[=4\left( x+\frac{ 3 }{ 2 } \right)^{2}-4*\frac{ 9 }{ 4 }+c\]
\[=4\left( x+\frac{ 3 }{ 2} \right)^{2}+c-9\]
If c-9=0 ,it is a perfect square.
or c=9

Answer 4

misprint,
\[make the co-efficient of x ^{2} as 1.\]