Question

find m so that x² + 4x + m is a complete square.
1) 8
2) -8
3) 4
4) 16

Answer 1

Answer:

4 is the answer

Step-by-step explanation:

(x)²+(x)(4)+(4)²

formula used:

(a+b)²

Answer 2

The value of m = 4 [ The correct option is 3) 4 ]

Given :

The expression x² + 4x + m

To find :

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

1) 8

2) - 8

3) 4

4) 16

Formula Used :

$\displaystyle \sf {(a + b) }^{2} = {a}^{2} + 2ab + {b}^{2}$

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

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

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

$\displaystyle \sf = {(x + 2)}^{2} - 4+ m\: \: \: \bigg[ \: \because \: {(a + b) }^{2} = {a}^{2} + 2ab + {b}^{2} \bigg]$

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

Since x² + 4x + m is a complete square

∴ m - 4 = 0

⇒ m = 4

So the required value of m = 4

Hence the correct option is 3) 4

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