Question

Which of the following is the complete list of roots for the polynomial function f (x) = (x squared + 6 x + 8) (x squared + 6 x + 13)?

Answer 1

`( {x}^(2) + 6x + 8)( {x}^(2) + 6x + 13) =0 \\`

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`{x}^(2) + 6x + 8 = 0`

`(x + 2)(x + 4) = 0`

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`x + 2 = 0`

`x = - 2`

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`x + 4 = 0`

`x = - 4`

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`{x}^(2) + 6x + 13 = 0`

`∆ = {b}^(2) - 4ac`

`a = coefficient \: \: of \: \: {x}^(2) = 1`

`b = coefficient \: \: of \: \: x = 6`

`c = the \: \: alone \: \: number \: = 13 \\`

Thus ;

`∆ = ({6})^(2) - 4 * (2) * (13)`

`∆ = 36 - 104`

`∆ = - 68`

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Point :

Remember from now on ,

In quadratic functions ;

if :

`∆ > 0`

The function has two roots

if :

`∆ = 0`

The function has just one root

if :

`∆ < 0`

The function doesn't have any root.

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Thus , ( x² + 6x + 13 ) doesn't have any root.

So ; ( x = - 2 ) & ( x = - 4 ) are the only roots.

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And we're done....♥️♥️♥️♥️♥️

Answer 2

c)-2,-4,-3+2i,-3-2i

Explanation:

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