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Helppppppppppppppppppppp

Helppppppppppppppppppppp-example-1
User Polarbear
by
8.0k points

2 Answers

8 votes

Answer:

see explanation

Explanation:

given a polynomial has roots x = a and x = b , then the corresponding factors are

(x - a) and (x - b)

the polynomial is then the product of the factors , that is

f(x) = (x - a)(x - b)

note that radical and complex roots occur in conjugate pairs.

(5)

given x = - 3i is a root then x = 3i is also a root

factors then are (x - 3i) , (x + 3i) , (x - 7) , then

f(x) = (x - 7)(x - 3i)(x + 3i) ← expand 2nd pair using foil

= (x - 7)(x² - 9i²) [ i² = - 1 ]

= (x - 7)(x² + 9) ← distribute factors

= x³ + 9x - 7x² - 63

f(x) = x³ - 7x² + 9x - 63

(6)

roots are x =
√(5) , x = -
√(5) , x = i , x = - i , and factors are

(x -
√(5) ) , (x +
√(5) ) , (x - i) , (x + i) and

f(x) = (x -
√(5) )(x +
√(5) )(x - i)(x + i) ← expand pairs of factors using FOIL

= (x² - 5)(x² + 1) ← distribute factors

=
x^(4) + x² - 5x² - 5

then

f(x) =
x^(4) - 4x² - 5

User Kalmas
by
8.2k points
8 votes

Answer:

I'd say think

Explanation:

Do 3i =(7²)

3i=49

User Daniel Rotter
by
8.2k points

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