Question

find m so that X2+4x+m is a complete square​

Answer 1

The value of m = 4

Given :

The expression x² + 4x + m

To find :

The value of m so that x² + 4x + m is a complete square

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is x² + 4x + m

Step 2 of 2 :

Find the value of m

$\displaystyle \sf{ {x}^{2} + 4x + m }$

$\displaystyle \sf{ = {x}^{2} + 2.x .2 + {2}^{2} - {2}^{2} + m }$

$\displaystyle \sf{ = {(x + 2)}^{2} - {2}^{2} + m }$

$\displaystyle \sf{ = {(x + 2)}^{2} + m - 4 }$

$\displaystyle \sf{ = {(x + 2)}^{2} +( m - 4 ) }$

Since x² + 4x + m is a complete square

∴ m - 4 = 0

⇒ m = 4

Hence the required value of m = 4

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