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Nookie1986 [14]
3 years ago
9

According to the fundamental theorem of algebra, how many roots does the polynomial f(x)=x4+3x2+7 have over the complex numbers,

and counting roots with multiplicity greater than one as distinct? (i.e f(x)=x2 has two roots, both are zero).
Mathematics
1 answer:
Finger [1]3 years ago
8 0

ANSWER

4 roots.

EXPLANATION

The given polynomial function is

f(x) =  {x}^{4}  + 3 {x}^{2}  + 7

This is a fourth degree polynomial.

According to the Fundamental Theorem of Algebra, an nth degree polynomial has n roots.

This roots include both real and complex roots.

Also repeated roots or roots with multiplicity greater than one are counted as distinct.

Since the given polynomial function is a fourth degree polynomial, the Fundamental Theorem of Algebra, says that this polynomial has 4 roots.

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3a x 5b x 7c = 39375, then find value of 7a - 2b + 3c​
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Answer:

Step-by-step explanation:

Simplifying

(7a + -2b) + -1[2(3a + -1c) + -3(2b + -3c)] = 0

Remove parenthesis around (7a + -2b)

7a + -2b + -1[2(3a + -1c) + -3(2b + -3c)] = 0

7a + -2b + -1[(3a * 2 + -1c * 2) + -3(2b + -3c)] = 0

7a + -2b + -1[(6a + -2c) + -3(2b + -3c)] = 0

7a + -2b + -1[6a + -2c + (2b * -3 + -3c * -3)] = 0

7a + -2b + -1[6a + -2c + (-6b + 9c)] = 0

Reorder the terms:

7a + -2b + -1[6a + -6b + -2c + 9c] = 0

Combine like terms: -2c + 9c = 7c

7a + -2b + -1[6a + -6b + 7c] = 0

7a + -2b + [6a * -1 + -6b * -1 + 7c * -1] = 0

7a + -2b + [-6a + 6b + -7c] = 0

Reorder the terms:

7a + -6a + -2b + 6b + -7c = 0

Combine like terms: 7a + -6a = 1a

1a + -2b + 6b + -7c = 0

Combine like terms: -2b + 6b = 4b

1a + 4b + -7c = 0

Solving

1a + 4b + -7c = 0

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-4b' to each side of the equation.

1a + 4b + -4b + -7c = 0 + -4b

Combine like terms: 4b + -4b = 0

1a + 0 + -7c = 0 + -4b

1a + -7c = 0 + -4b

Remove the zero:

1a + -7c = -4b

Add '7c' to each side of the equation.

1a + -7c + 7c = -4b + 7c

Combine like terms: -7c + 7c = 0

1a + 0 = -4b + 7c

1a = -4b + 7c

Divide each side by '1'.

a = -4b + 7c

Simplifying

a = -4b + 7c

8 0
2 years ago
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