Question

(ii) x2 - 3./3x + 6 = 0​

Answer 1

An2-3x-6=0  

Three solutions were found :

x = 2

x =(-3-√-15)/4=(-3-i√ 15 )/4= -0.7500-0.9682i

x =(-3+√-15)/4=(-3+i√ 15 )/4= -0.7500+0.9682i

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((2x3 -  x2) -  3x) -  6  = 0  

Step  2  :

Checking for a perfect cube :

2.1    2x3-x2-3x-6  is not a perfect cube

Trying to factor by pulling out :

2.2      Factoring:  2x3-x2-3x-6  

Thoughtfully split the expression at hand into groups, each group having two terms :

Group 1:  -3x-6  

Group 2:  2x3-x2  

Pull out from each group separately :

Group 1:   (x+2) • (-3)

Group 2:   (2x-1) • (x2)

Bad news !! Factoring by pulling out fails :

The groups have no common factor and can not be added up to form a multiplication.

Polynomial Roots Calculator :

2.3    Find roots (zeroes) of :       F(x) = 2x3-x2-3x-6

Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two

Step-by-step explanation: