What does the fundamental theorem of algebra illustrate?

Step-by-step explanation:

The "fundamental theorem of algebra" tells you a polynomial has a number of roots equal to its degree. Those roots are not always rational or real, but are always members of the set of complex numbers.

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The given equation can be put into vertex form as ...

  2(x -1)^2 -3 = 0

It will have roots ...

  1 ± √(3/2) = (2±√6)/2

If you don't like to mess with translating a quadratic to vertex form, you can use the quadratic formula:

  x = (-b±√(b²-4ac))/(2a) . . . . . for a=2, b=-4, c=-1

  x = (4 ± √(16+8))/(2·2) = (4 ± 2√6)/4 = (2±√6)/2

since proposition states that a number is greater than 25, if is true then the number must actually be greater than 25.

this implies that all possible options, except 24, can be accepted

you probably already have the answer but anyways it's b. 15.0

step-by-step explanation: