Answer:
As (1, 0), (4, 0) and (6, 0) are the x-intercepts, as shown in figure a.
Hence, the real solutions are: (x - 1), (x - 4) and (x - 6) i.e. x = 1, 4 and 6.
Step-by-step explanation:
As the given equation is: x³ - 11x² + 34x - 24 = 0
To find x-intercept, we need to plot the graph where y is equal to zero.
i.e. y = 0
The x³ - 11x² + 34x - 24 = 0 will have the solution where the graph touches the x-axis.
So, we need to draw the graph to observe the x-intercept, checking the points where y = 0.
The figure a shows the required graph. The points where y = 0 are the x-intercepts. So, the points where y = 0 have x values such as 1, 4 and 6.
So, (1, 0), (4, 0) and (6, 0) are the x-intercepts, as shown in figure a.
So, the real solutions are: (x - 1), (x - 4) and (x - 6) i.e. x = 1, 4 and 6.
Keywords: x-intercept, real solution, equation
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