Question

Which graph represents the solution set for the quadratic inequality x2 + 2x + 1 > 0?

Answer 1

Answer:

C

Step-by-step explanation:

Answer 2

Answer:

We have to determine the graph of the given inequality as:

$x^2+2x+1>0$

on solving this equation we get:

$(x+1)^2>0$

Since we know that:

$(x+1)^2=x^2+1^2+2\times x\times 1\\\\(x+1)^2=x^2+1+2x$

Now we know that when $x=-1$ the value of:

$(x+1)^2=0$

Also for the value other than -1 the function being a quadratic function will always give a non-zero positive value.

Hence, range of the function in intervals could be written as:

(-∞,-1)∪(-1,∞).

Hence, the graph of the function will be the whole of the number line with a open circle on -1.