Math, asked by Gunia9987, 8 months ago

Find the root of 6y-5y square =0
By factorisation

Answers

Answered by magimagi
0

hey m8,

6y2-5y-6=0

Two solutions were found :

y = -2/3 = -0.667

y = 3/2 = 1.500

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 ((2•3y2) -  5y) -  6  = 0

Step  2  :

Trying to factor by splitting the middle term

2.1     Factoring  6y2-5y-6

The first term is,  6y2  its coefficient is  6 .

The middle term is,  -5y  its coefficient is  -5 .

The last term, "the constant", is  -6

Step-1 : Multiply the coefficient of the first term by the constant   6 • -6 = -36

Step-2 : Find two factors of  -36  whose sum equals the coefficient of the middle term, which is   -5 .

     -36    +    1    =    -35

     -18    +    2    =    -16

     -12    +    3    =    -9

     -9    +    4    =    -5    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -9  and  4

                    6y2 - 9y + 4y - 6

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

                   3y • (2y-3)

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

                   2 • (2y-3)

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

                   (3y+2)  •  (2y-3)

            Which is the desired factorization

Equation at the end of step  2  :

 (2y - 3) • (3y + 2)  = 0

Step  3  :

Theory - Roots of a product :

3.1    A product of several terms equals zero.

When a product of two or more terms equals zero, then at least one of the terms must be zero.

We shall now solve each term = 0 separately

In other words, we are going to solve as many equations as there are terms in the product

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

3.2      Solve  :    2y-3 = 0

Add  3  to both sides of the equation :

                     2y = 3

Divide both sides of the equation by 2:

                    y = 3/2 = 1.500

Solving a Single Variable Equation :

3.3      Solve  :    3y+2 = 0

Subtract  2  from both sides of the equation :

                     3y = -2

Divide both sides of the equation by 3:

                    y = -2/3 = -0.667

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