Question

Exercise 3.3: Nonlinear equations 1. Find the zeros of the following functions graphically: b) g\left(x\right)=2x^2-4x-16 4 c) For the following function determine if x = 1 is a root: 5. Find the rational roots, if any, of the following: b) 8x^3+6x^2-3x-1=0 6. Find the equilibrium solution for each of the following models: a) Q_d=Q_s Q_d=3-P^2 Q_s=6P-4

Answer 1

Answer :

3.3) Given function

G(x)=2x^2-4x-16

To find zero of above function

2x^2-4x-16=0

2x^2-8x+4x-16=0

2x*(x-4)+4*(x-4)=0

(2x+4)*(x-4)=0

X=4 or -4/2=-2

5) Given function

8x^3+6x^2-3x-1=0

If X=1 then above function has a value

8*1^3+6*1^2-3-1=10

Since at X=1 we are getting non zero value so X=1 is not root of above equation.

Rearranging above equation

8x^3-1+6x^2-3x=0

(2x-1)*(4x^2+1+2x)+3x*(2x-1)=0

(2x-1)*(4x^2+2x+1+3x)=0

(2x-1)*(4x^2+5x+1)=0

(2x-1)*(4x^2+4x+x+1)=0

(2x-1)*((4x*(x+1)+1*(x+1))=0

(2x-1)*(4x+1)*(x+1)=0

X=1/2 or -1/4 or -1

6)

Given Qd=Qs

3-P^2=6P-4

P^2+6P-7=0

P^2+7P-P-7=0

P*(P+7)-1*(P+7)=0

(P-1)*(P+7)=0

P=1 or -7

Since price is always positive so P=1

And Qd=3-1^2=2

Qs=6*1-4=2