Question

Solve the Quadratic equation by formula method: a) 6x2 – 29x + 35 = 0

Answer 1

Answer:

The first term is,  6x2  its coefficient is  6 .

The middle term is,  +29x  its coefficient is  29 .

The last term, "the constant", is  +35 

Step-1 : Multiply the coefficient of the first term by the constant   6 • 35 = 210 

Step-2 : Find two factors of  210  whose sum equals the coefficient of the middle term, which is   29 .

     -210   +   -1   =   -211     -105   +   -2   =   -107     -70   +   -3   =   -73     -42   +   -5   =   -47     -35   +   -6   =   -41     -30   +   -7   =   -37     -21   +   -10   =   -31     -15   +   -14   =   -29     -14   +   -15   =   -29     -10   +   -21   =   -31     -7   +   -30   =   -37     -6   +   -35   =   -41     -5   +   -42   =   -47     -3   +   -70   =   -73     -2   +   -105   =   -107     -1   +   -210   =   -211     1   +   210   =   211     2   +   105   =   107     3   +   70   =   73     5   +   42   =   47     6   +   35   =   41     7   +   30   =   37     10   +   21   =   31     14   +   15   =   29   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  14  and  15 

                     6x2 + 14x + 15x + 35

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

                    2x • (3x+7)

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

                    5 • (3x+7)

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

                    (2x+5)  •  (3x+7)

             Which is the desired factorization

Step-by-step explanation:

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