2. The city of Johnsonville was 1.5 inches of rain short of the normal amount for the year at the end of July. During the

According to the Fundamental Theorem of Algebra, which polynomial function has exactly 8 roots?f(X) 3x4 +2xfox)- (6x -4x5-10 3x2

mina [271]

Answer:
A. (3x²-4x-5)(2x⁶-5)

Explanation:
The fundamental theorem of Algebra states that:
"A polynomial of degree 'n' will have exactly 'n' number of roots"

We know that the degree of the polynomial is given by the highest power of the polynomial.
Applying the above theorem on the given question, we can deduce that the polynomial that has exactly 8 roots is the polynomial of the 8th degree

Now, let's check the choices:
A. (3x²-4x-5)(2x⁶-5)
The term with the highest power will be (3x²)(2x⁶) = 6x⁸
Therefore, the polynomial is of 8th degree which means it has exactly 8 roots. This option is correct.

B. (3x⁴+2x)⁴
The term with the highest power will be (3x⁴)⁴ = 81x¹⁶
Therefore, the polynomial is of 16th degree which means it has exactly 16 roots. This option is incorrect.

C. (4x²-7)³
The term with the highest power will be (4x²)³ = 64x⁶
Therefore, the polynomial is of 6th degree which means that it has exactly 6 roots. This option is incorrect

D. (6x⁸-4x⁵-1)(3x²-4)
The term with the highest power will be (6x⁸)(3x²) = 18x¹⁰
Therefore, the polynomial is of 10th degree which means that it has exactly 10 roots. This option is incorrect

Hope this helps :)

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2 years ago

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The graph of y=3x^2-3x-1 is shown. Use the graph to find estimates for the solutions of i)3x^2-3x+2=2 ii) 3x^2-3x-1=x+1

AlexFokin [52]

Answer:

i) (0, 2) and (1, 2), ii) (0.333, 1.333) and (1, 2).

Step-by-step explanation:

i) Let be $y=3\cdot x^{2}-3\cdot x -1$ , if $3\cdot x^{2}-3\cdot x +2 = 2$ , which is equivalent to the following system of equations:

$y = 3\cdot x^{2}-3\cdot x +2$

$y = 2$

Now, this system is now represented by means of a graphing tool and whose outcome is attached below. There are two solutions: (0, 2) and (1, 2)

ii) Let be $y=3\cdot x^{2}-3\cdot x -1$ , if $3\cdot x^{2}-3\cdot x +2 = x+1$ , which is equivalent to the following system of equations:

$y = 3\cdot x^{2}-3\cdot x +2$

$y = x+1$

Now, this system is now represented by means of a graphing tool and whose outcome is attached below. There are two solutions: (0.333, 1.333) and (1, 2)