3x^3-35x^2+150x-250=0, find the value of x

Question

I need the answer asap

Answer 1

3x³ - 35x² + 150x - 250 = 0

 

The use the rational root test first.

 

For the candidates ±A/B: a is a factor of 250 and B is a factor of 3. There are 32 candidates.

 

Note that when x < 0, all terms are negative, so you can discard the 16 negative candidates.

 

Testing them shows x = 5 is a root. Factor x-5 out.

 

3x³ - 35x² + 150x - 250 = (x - 5)(3x² - 20x + 50)

 

Set the other factor to 0 and use the quadratic formula to get the other roots.

 

x = [-(-20) ±√((-20)² - 4·3·50)] / (2·3)

 

= [20 ±√(-200)] / 6

 

= 10/3 ± (5√2 / 3) i

Answer 2

By trial and error, I found that x=5 is a solution. The polynomial factors into (x-5)(3x²-20x+50)

 

If you can include complex numbers, you can use the Quadratic Formula to solve the remaining  3x2-20x+50 = 0

 

x = [-(-20)±√((-20)² - 4(3)(50))]/2(3) = [20 ±√(400-600)]/6 = (20 ±√(-200))/6 = [20 ± 10i√2]/6

 

If you haven't studied complex numbers, then x=5 is the only solution.