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mafiozo [28]
3 years ago
13

What are the solutions of this equation? x^ - x - 56 = 0

Mathematics
2 answers:
NikAS [45]3 years ago
8 0

Answer:

y = 0

Step-by-step explanation:

Lady_Fox [76]3 years ago
3 0

\large\bf{\underline{Solutions:}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{⟹8 , -7}

__________________________________________

\large\bf{\underline{Given\: equation :}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{⟹ x^2 -8x-56 }

__________________________________________

\large\bf{\underline{Using\: middle\:term\: splitting}}

\large\bf{Here, a = 1 , b = 1 \:and \:c= 56 }

\large\bf{ ⟹ a\times c = 1\times56 =56}

  • Therefore we need two terms which on adding or subtracting with each other gives 56 and on multiplying gives 56

__________________________________________

\large\bf{\underline{By\: splitting \:the\:middle\:term:}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{⟹x^2-8x+7x-56}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{⟹x(x-8)+7(x-8}

‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{⟹(x-8)(x+7)}

\large\bf{\underline{Hence}}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{⟹x-8=0}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{⟹x=0+8}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{⟹x=8}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎and

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{⟹x+7=0}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{⟹x=0-7}

‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎‎‎ ‎ ‎\large\bf{⟹x=-7}

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I'm sure you want your functions to appear as perfectly formed as possible so that others can help you.  f(x) = 4(2)x should be written with the " ^ " sign to denote exponentation:  f(x) = 4(2)^x

                                                                                      f(b) - f(a)

The formula for "average rate of change" is a.r.c. = --------------

                                                                                           b - a

                                    change in function value

This is equivalent to  ---------------------------------------

                                            change in x value

For Section A:  x changes from 1 to 2 and the function changes from 4(2)^1 to  4(2)^2:  8 to 16.  Thus, "change in function value" is 8 for a 1-unit change in x from 1 to 2.  Thus, in this Section, the a.r.c. is:

                 8

               ------ = 8 units    (Section A)

                  1

Section B:  x changes from 3 to 4, a net change of 1 unit:  f(x) changes from

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        224 units

      ----------------- = 224 units (Section B)

            1 unit

The a.r.c for Section B is 28 times greater than the a.r.c. for Section A.

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