Question

find the roots of the following. 3x2 -5x +2=0​

Answer 1

Answer:

Step-by-step explanation:

3x2-x-2=0  

Two solutions were found :

x = -2/3 = -0.667

x = 1

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (3x2 -  x) -  2  = 0  

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  3x2-x-2  

The first term is,  3x2  its coefficient is  3 .

The middle term is,  -x  its coefficient is  -1 .

The last term, "the constant", is  -2  

Step-1 : Multiply the coefficient of the first term by the constant   3 • -2 = -6  

Step-2 : Find two factors of  -6  whose sum equals the coefficient of the middle term, which is   -1 .

     -6    +    1    =    -5  

     -3    +    2    =    -1    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -3  and  2  

                    3x2 - 3x + 2x - 2

Step-4 : Add up the first 2 terms, pulling out like factors :

                   3x • (x-1)

             Add up the last 2 terms, pulling out common factors :

                   2 • (x-1)

Step-5 : Add up the four terms of step 4 :

                   (3x+2)  •  (x-1)

            Which is the desired factorization

Answer 2

Answer:

x = 2/3 , 1

Step-by-step explanation:

$3x^{2} -5x +2 =0$

= $x^{2} -5x/3 = -2/3$

=$(x^{2} - 5/6)$^2 = -2/3 + (5/6)^2

=$(x + 5/6)^2 = 1/36$

=$x - 5/6 = 1/6, - 1/6$

=$x = 1/6 + 5/6 , -1/6 + 5/6$

= $x = 1 , 2/3$