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crimeas [40]
3 years ago
9

Let f(x)= x^2-4x-c. Find a nonzero value of c such that f(c)=c.​

Mathematics
1 answer:
Dimas [21]3 years ago
5 0

Answer:

The nonzero value of c will be:

  • c = 6

Step-by-step explanation:

Given the function

f\left(x\right)=\:x^2-4x-c

f\left(c\right)=\:c^2-4c-c

as

f(c) = c

so

c=\:c^2-4c-c

switching the sides

c^2-4c-c=c

subtract c from both sides

c^2-4c-c-c=c-c

c^2-6c=0

c\left(c-6\right)=0

Using the zero factor principle

\:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)

c=0\quad \mathrm{or}\quad \:c-6=0

so, the solutions to the quadratic equations are:

c=0,\:c=6

Therefore, a nonzero value of c will be:

  • c = 6
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