Solve: 6p+2=p^2+3p^3

Question

Double checking my work. Solve quadratic equation: 6p+2=p^2+3p^3

 

6p+2=p^2+3p^3

6p+2=3p^3+p^2

6p+2−(3p^3+p^2)=3p^3+p^2−(3p^3+p^2)
−3p^3−p^2+6p+2=0
(−3p−1)(p^2−2)=0
−3p−1=0 or p^2−2=0

 

answer is P=-1\3

Answer 1

6P + 2 = P² + 3P²

 

3P³ + P² -6P -2 =0 (Polynomial equation)

 

-1/3 is a factor of the polynomial. This means that 3(1/3)³ + (1/3)² -6(1/3) -2 =0

 

 

P+1/3 goes into 3P³ + P² -6P -2 =0 with a factor of 3P² - 6

 

So we have (P + 1/3) (3P² - 6)

 

This gives us P+1/3 =0 or 3P² -6 = 0

 

So P=-1/3 or 3P²=6, which gives P²=2 or P²-2=0, P²=2, P = 2^(1/2) = √2

 

P=-1/3 or P =-1.4142 or P =1.4142