Respuesta :

mbh292
The plus-minus sign represents that there are two possible outcomes.

In this case, we have [tex]1 \pm \sqrt{5} [/tex]. When we branch out the possibilities we got 2 values: [tex]1 + \sqrt{5} [/tex] and [tex]1 - \sqrt{5} [/tex]

Those are the roots of this equation. When they ask their product, they want you to multiply both numbers.

When we multiply them: [tex](1 + \sqrt{5}) \times( 1 - \sqrt{5}) [/tex]

When we FOIL the we get: [tex]1 \times 1 - 1 \times \sqrt{5} + 1 \times \sqrt{5} - \sqrt{5} \times \sqrt{5} [/tex]

Simplify:
[tex]1 - \sqrt{5} + \sqrt{5} - 5[/tex]
[tex]1 - 5 = 6[/tex]

So the product of the two roots of this equation is 6.
chetankachana

Answer:

-4

Step-by-step explanation:

Hello!

The two roots of the quadratic are [tex]1 + \sqrt5[/tex] and [tex]1 - \sqrt 5[/tex].

We can utilize the Difference of Squares (DOS) formula for simple multiplication.

DOS formula: [tex]a^2 - b^2 = (a + b)(a - b)[/tex]

Multiply:

  • [tex](1 + \sqrt5)(1 - \sqrt5)[/tex]
  • [tex](1^2) - (\sqrt5)^2[/tex]
  • [tex]1 - 5[/tex]
  • [tex]-4[/tex]

The product of the two roots is -4.

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