Question

find the sum of zeroes of 4x^2+9x-13​

Answer 1

The first term is,  4x2  its coefficient is  4 .

The middle term is,  -9x  its coefficient is  -9 .

The last term, "the constant", is  -13 

Step-1 : Multiply the coefficient of the first term by the constant   4 • -13 = -52 

Step-2 : Find two factors of  -52  whose sum equals the coefficient of the middle term, which is   -9 .

     -52   +   1   =   -51     -26   +   2   =   -24     -13   +   4   =   -9   That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -13  and  4 

                     4x2 - 13x + 4x - 13

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

                    x • (4x-13)

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

                     1 • (4x-13)

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

                    (x+1)  •  (4x-13)

             Which is the desired factorization