1. If A = 3 and B = 4 + i, A/B = ?

Question

1. If A = 3 and B = 4 + i, A/B = ?

 

2. The graph of f(x) = 6x⁵ – 5x⁴ + 12x³ +8x² +2x + 9 would have, at most, how many x-intercepts?

Answer 1

1)

 

A / B = 3 / (4 + i)

 

 

Since we have a complex number in the denominator, we want to multiply the expression by its conjugate, (4 - i), so that the denominator is a real number.

 

[3 / (4 + i)] * [(4 - i) / (4 - i)] =

 

(12 - 3i) / (16 - i²) =

 

(12 - 3i) / (16 - (-1)) =

 

(12 - 3i) / 17

 

 

 

2)

 

The number of x-intercepts depends on the degree of f(x).  Since f(x) is a degree of 5, f(x) would have at most 5  x-intercepts. 

 

x-intercepts can also be found by setting f(x) equal to zero, and solving for x.  The x values you obtain when solving are your x-intercepts.  Keep in mind that these x values may repeat.  Nevertheless, they are still x-intercepts.  The only difference is that f(x) is tangential to the x-axis at the repeating x values.