We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
132
1
avatar+462 

1.

 

2.

 

 Oct 1, 2018
 #1
avatar+4775 
+1

a) Yes, as long as a and b are allowed to be complex numbers.  Consider the simple parabola

 

\(y = x^2+1 \\ \text{with complex roots } \pm i \\ \text{this can be written as }\\ (x-i)(x+i) = x^2 +i x - i x +(i)(-i) = x^2+1\)

 

b) No.  Consider a general cubic polynomial

 

\(y = a x^3 + b x^2 + c x + d\)

 

\(\text{as }x \to -\infty, \text{the }x^3 \text{ term dominates everything and }y \to -\infty \\ \text{as }x \to +\infty, \text{ likewise the }x^3 \text{ term dominates and }y \to +\infty \\ \text{somewhere along the way it's got to cross the x axis and at that point }\\ y=0 \text{ at a real value of x}\)

.
 Oct 1, 2018

5 Online Users

avatar