The difference between roots of the quadratic equation x^2+x+c=0 is 6. find c.

.

Step-by-step explanation:

Let the smaller root to this equation be . The larger one will equal .

By the factor theorem, this equation is equivalent to

, where .

Expand this expression:

.

This equation and the one in the question shall differ only by the multiple of a non-zero constant. It will be helpful if that constant is equal to . That way, all constants in the two equations will be equal; will  be equal to .

Compare this equation and the one in the question:

The coefficient of in the question is (which is omitted.) The coefficient of in this equation is . If all corresponding coefficients in the two equations are equal to each other, these two coefficients shall also be equal to each other. Therefore .

This equation will become:

.

Similarly, for the coefficient of ,

.

.

This equation will become:

.

is the value of the constant term of this quadratic equation.

1 + (6 / x - 1)

step-by-step explanation:

divide using polynomial division.

8

step-by-step explanation: