Find all zeros of p(x). Include any multiplicities greater than 1.

Question

p(x)=3x^3-10x^2+10x-4

Answer 1

 

p(1) = 3 -10 + 10 -4 # 0       p(-1) = -3 -10 -10 -4 #0   

 

p(2) = 24-40+20-4 =0 ----->

 

p(x) = (x-2)(3x² - 4x+2) ; delta = (-4)² - 4(3)(2) = -8  for 3x² -4x +2

 

therefore, no more factors, assuming we're working within R , the set of real numbers.

 

ONLY ONE ZERO IN R FOR p(x), THAT IS  x = 2

 

 

 

Answer 2

use trial and error with factors of 3 and 4

2 is a zero

(x-2)(3x²-4x+2)

using the quadratic equation

4+√(16-24)/6

4+√-8/6

(4+2√2i)/6

(2+√2i)/3

(x-[2-√2i]/3)(x-[2+√2i]/3)(x-2)

Answer 3

Lexi, you can graph the equation and find out that it intersects the x-axis at (approximately) x=3/10. I hope this helps you