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another way to present the fundamental theorem of algebra is to state that, "for any polynomial equation of degree n with real coefficients, there exist n complex solutions." why is it important to learn about complex solutions? why is it remarkable that with real coefficients, there must be complex solutions?

answer:

1. imaginary numbers, also called complex numbers, are used in real-life applications, such as electricity, as well as quadratic equations. ac electricity changes between positive and negative in a sine wave. combining ac currents can be very difficult because they may not match properly on the waves.

2. a polynomial of degree n can have only an even number fewer than n real roots. thus, when we count multiplicity, a cubic polynomial can have only three roots or one root; a quadratic polynomial can have only two roots or zero roots.

the answer is d. 75%

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.