question_answer

The graph of \[{{\text{x}}^{\text{2}}}+\text{4}=0:\]

A) intersects X-axis at two distinct points

B) touches X-axis at a point

C) neither touches nor intersects X-axis

D) either touches or intersects X-axis.

Correct Answer: C

Solution :

The graph of \[{{x}^{2}}+4=0\]

The\[{{x}^{2}}\]is positive so the general shaph is ‘U’. Since the coefficient of x is zero so the graph is central about the Y-axis. The constant part of the equation is of value \[+4,\] so it lifts the vertex up from \[y=0\] to\[y=4\].

\[\therefore \] The graph of \[{{x}^{2}}+4=0,\] neither touches nor intersects X-axis.

So, option [c] is correct.