Which of the following is not a solution to the following equation?
x^3-5x^2+4 = 0
x = 0
x = 4.83
x = -0.83
x = 1
0^3 - 5 0^2 + 4 = 4 not 0
1 works
so factor it out
(x-1)(x^2-4x-4) = 0
solve that quadratric
x = [ 4 +/- sqrt(16+16)]/2
= 2 +/- 2.83
= 4.83 and -.83 sure enough
Thanks!
To determine which of the given values is not a solution to the equation x^3 - 5x^2 + 4 = 0, you can substitute each value into the equation and check if it yields the equation to be true.
Let's go through each given value one by one:
1. x = 0:
Substituting x = 0 into the equation, we get:
(0)^3 - 5(0)^2 + 4 = 0
0 - 0 + 4 = 0
4 = 0 (Not true)
2. x = 4.83:
Substituting x = 4.83 into the equation, we get:
(4.83)^3 - 5(4.83)^2 + 4 = 0
112.1803 - 116.7545 + 4 = 0
0.4258 - 116.7545 + 4 = 0
-112.3287 + 4 = 0
-108.3287 = 0 (Not true)
3. x = -0.83:
Substituting x = ‐0.83 into the equation, we get:
(-0.83)^3 - 5(-0.83)^2 + 4 = 0
-0.5719887 - 3.3155 + 4 = 0
-0.5719887 -3.3155 + 4 = 0
0.1125113 - 3.3155 + 4 = 0
-3.2039887 + 4 = 0
0.7960113 = 0 (Not true)
4. x = 1:
Substituting x = 1 into the equation, we get:
(1)^3 - 5(1)^2 + 4 = 0
1 - 5 + 4 = 0
0 = 0 (True)
Based on the calculations, we find that x = 0, x = 4.83, and x = -0.83 are NOT solutions to the equation x^3 - 5x^2 + 4 = 0. Thus, the correct answer is: x = 1.