Solve the equation $x ^ { 3 } - 12 x ^ { 2 } + 41 x - 30 = 0$ graphically in the interval $[ - 1,7 ]$.
A) $x = 1.00 , x = 5.00 , x = 3.50$
B) $x = 1.00 , x = 5.00 , x = 6.00$
C) $x = 0.50 , x = 5.50 , x = 3.50$
D) $x = 1.00 , x = 5.50 , x = 6.00$
E) $x = 0.50 , x = 5.00 , x = 6.00$

Question

Quizplus · Accepted Answer

To solve the equation graphically, one would plot the function $f(x) = x^3 - 12x^2 + 41x - 30$ and look for the points where the graph crosses the x-axis within the interval $[-1,7]$. The correct roots, $x = 1.00$, $x = 5.00$, and $x = 6.00$, are the x-coordinates of these points of intersection, which correspond to the real solutions of the equation.

Solve the Equation x3−12x2+41x−30=0x ^ { 3 } - 12 x ^ { 2 } + 41 x - 30 = 0x3−12x2+41x−30=0

Solve the Equation $x ^ { 3 } - 12 x ^ { 2 } + 41 x - 30 = 0$