A) Show that the equation x^3 + 6x - 5 = 0 has a solution between x = 0 and x = 1

Since , there is a solution for between and .

Step-by-step explanation:

A solution of the polynomial is a root such that sign of dependent value changes, either from positive to negative or from negative to positive. Let , is a solution of the equation if and only if . We proceed to evaluate the function at each bound:

x = 0

x = 1

Since , there is a solution for between and .

y=mx+b

step-by-step explanation:

m is slope, b is y-intercept

infinitely many solutions

step-by-step explanation:

we have been given the equation;

2(2x + 3) = -4 + 2(2x + 5)

we need to determine the value of x.

2(2x + 3), we expand this expression to obtain 4x + 6

similarly 2(2x + 5) will become 4x + 10

now we have;

4x + 6 = -4 + 4x + 10

4x + 6 = 4x + 10 - 4

4x + 6 = 4x + 6

the expression on the left hand side is identical to the one on the right hand side. therefore, we are looking at just a single straight line whose equation is;

y = 4x + 6

consequently, we shall have infinitely many solutions