Question

Which of the following is a valid conclusion for the problem x2 + 6x + 8 = 0?

x - 3 = 0 and x + 5 = 0
x + 4 = 0 and x - 2 = 0
x + 4 = 0 and x + 2 = 0
x - 4 = 0 and x + 2 = 0

Answer 1

the correct answer is x+4=0 and x+2=0 

Answer 2

Answer:

option (3) is correct.

$\Rightarrow (x+2)=0$  or $\Rightarrow (x+4)=0$

Step-by-step explanation:

Given quadratic equation $x^2+6x+8=0$

We have to choose a valid conclusion for the problem  $x^2+6x+8=0$

Consider the given quadratic equation  $x^2+6x+8=0$ .

We can solve the quadratic equation using middle term split,

6x can be written as 2x +4x  , thus equation becomes,

$x^2+6x+8=0$

$\Rightarrow x^2+2x+4x+8=0$

Taking x common from first two term and 4 common from last two terms, we have,

$\Rightarrow x(x+2)+4(x+2)=0$

$\Rightarrow (x+4)(x+2)=0$

Using zero product property, $a\cdot b=0 \Rightarrow a=0 \ or \ b=0$ ,we have,  

$\Rightarrow (x+2)=0$  or $\Rightarrow (x+4)=0$

Thus, option (3) is correct.