Question

To solve it, we can find the characteristic polynomial and use the initial conditions to determine the constants. The characteristic polynomial is given by:r4−4r3+4r2=0

Now, let's factor this polynomial:
r2(r2−4r+4)=0
The roots of this polynomial are r=0 with multiplicity 2 and r=2 with multiplicity 2.

Answer 1

To find the solutions to the quadratic equation x² +0.0211x -0.0211 = 0, you can use the quadratic formula. The solutions are approximately -0.028511249 and 0.007411249.

Step-by-step explanation:

This is an equation in one variable, so we can solve for the unknown value using the quadratic formula. The equation is given by x² +0.0211x -0.0211 = 0. To find the solutions, we can plug the coefficients into the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

Plugging in the values, we have:

x = (-0.0211 ± √(0.0211² - 4(1)(-0.0211)) / (2(1)) = (-0.0211 ± √(0.00044421 + 0.000844) / 2 = (-0.0211 ± √0.00128821) / 2 = (-0.0211 ± 0.035922499) / 2 = -0.028511249 or 0.007411249