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

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) $x = 0.50 , x = 5.00 , x = 6.00$

Quizplus · Accepted Answer

To solve the equation graphically, one would plot the function $f(x) = x^3 - 12x^2 + 41x - 30$ and find the x-values where the graph crosses the x-axis within the given interval. Without plotting, we can't directly verify the solutions graphically here, but we can use the Rational Root Theorem or synthetic division to test the given options. Among the choices, $x = 1, x = 5, x = 6$ are the roots that satisfy the equation, as they make the polynomial equal to zero. This can be verified by substituting these values into 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 $x ^ { 3 } - 12 x ^ { 2 } + 41 x - 30 = 0$