Which are the solutions of x^2 = -13x – 4?

Step-by-step explanation:

Rewrite this equation in standard quadratic form:  x^2 + 13x + 4 = 0.

Here the coefficients are 1, 13 and 4, so the discriminant is

b^2-4ac, or 169 - 4(1)(4) = 153

Since the discriminant is + there are two real, unequal roots.  They are:

       -13 ± √153

x =  

            2

x =

a² + b²= c²

24² + 7² = c²

c= 25

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.