Hi there! See an attachment below! (May not be clear for an explanation so I will explain it to you.)
We can find real roots of polynomial function by counting their x-intercepts of graph. See in the attachment that the graph intersects 3 points on x-axis/plane.
x-axis represents the solutions of the graph or equation of the graph. For example, a graph of (x-1)² would be a parabola that has x-intercept at (1,0). If we solve the equation for (x-1)² = 0, our solution would be x = 1 like the x-intercepts.
Conclusions
- We can find the real roots of the graph by counting how many points does the graph intersect on x-axis/plane.
- If a graph doesn't intersect x-axis or does not have any points on x-axis, that graph or its equation does not have a real root. For example, graph of x²+1
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