Question

4s^3 +30s² + 74s+ 78 = 0
S = - 4.2 ,- 1.649 +j1.386 ,- 1.649 - j 1. 386
I need to understand how value of s is finded.​

Answer 1

Answer:

Step-by-step explanation:

The equation that you just gave was a cubic equation, first of all let's talk about a quadratic equation. It is in the form

ax²+bc+c=0, where a and b are coefficient

For this equation

x=(-b±√(b²-4ac))÷2a

When (b²-4ac) is positive i.e. 4ac is smaller than b², the answer is a real number

But when b²-4ac is negative i.e.4ac is larger than b² we get a complex solution

For ex. √4=2, but what about √-4?

We take √-4=2i, where i=√-1, i is not a real number

In the case of cubic equation we know that it has 3 solutions. Complex numbers are always is pair, thus there can be 2 types of solutions, 1) when we get 3 real soultions, 2) when we get 1 real and 2 unreal solution

In your case we first plot the cubic equation on the graph. The point of graph of equation which intersects the x-axis will be one solution. Let's suppose that point is -4.2, we divide 4s³+30s²+74s+78 by (x+4.2), and then apply the quadratic equation formula discussed earlier