Question

1. choose the best answer. given the equation, ( y = x^2 + 4 ), the range, or y-values, will always be greater than or equal to 4, and the graph will never intersect the x - axis. what will be the nature of the roots of ( y = x^2 + 1 )? one root at -1 no real roots one root at 1 two roots, at 1 and -1 10) find the real roots of ( y = x^3 - 5x^2 + x - 5 ) by inspecting the graph: 11) what is ( f(0) ) (x)?

Explanation:

Step1: Analyze the first question

We inspect the graph of $y = x^3 - 2x^2 + x - 1$. The real roots are the x-values where the graph crosses the x-axis. Looking at the graph, it crosses the x-axis at $x=1$.

Step2: Analyze the second question

For $y = x^2 + 4$, we check if $y=0$ has real solutions. Set $x^2 + 4 = 0$, so $x^2 = -4$. Since squares of real numbers are non-negative, there are no real $x$ values that satisfy this. The graph never intersects the x-axis, so there are no real roots.

Answer:

1. The real root is $\boldsymbol{1}$
2. $\boldsymbol{No\ real\ roots}$