Write a quadratic equation with the given roots. write the equation in the form of ax^2+bx+c=0 where a b and c are integers

You haven't provided the required roots, but I can tell you how to do this kind of exercises in general.

If the coefficient is 1, i.e. the equation is written like , then you can say the following about the coefficients b and c:

So, for example, if we want an equation whose roots are 4 and -2, we have:

So, the equation is

If your roots are rational, you can work like this: suppose you want an equation with roots 3/4 and 1/2. You have:

And so the equation is

In order to have integer coefficients, you can multiply both sides of the equation by 8:

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.