Question

Find the roots of polynomial equation. 2x^3+2x^2-19x+20=0

Answer 1

Without using CAS?

Answer 2

Without using CAS, it would look something like this: \[2x^3+2x^2-19x+20=0\]
Factor the left hand side:(factors into a product with 2 terms) \[(x+4)(2x^2-6x+5)=0\] Solve each product separatly: \[x+4=0 <=> x=-4\] \[2x^2-6x+5=0\] This equation has 0 real solutions only imaginary solutions. This can be seen by calculating the discriminant:\[D=b^4-4*a*c=(-6)^2-4*2*5=-4\] When D is below 0, there is only 2 imaginary solutions. (When D is 0, there is 1 solutions, and when D is above 0 there is 2 solutions.)

Answer 3

Hope it helps @Pagen13