Question

If the roots of a quadratic equation are 1±√5, then the product of the roots is

Answer 1

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

In this case, we have
`1 \pm √(5)`. When we branch out the possibilities we got 2 values:
`1 + √(5)` and
`1 - √(5)`

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

When we multiply them:
`(1 + √(5)) *( 1 - √(5))`

When we FOIL the we get:
`1 * 1 - 1 * √(5) + 1 * √(5) - √(5) * √(5)`

Simplify:

`1 - √(5) + √(5) - 5`

`1 - 5 = 6`

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

Answer 2

-4

Explanation:

Hello!

The two roots of the quadratic are
`1 + \sqrt5` and
`1 - \sqrt 5`.

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

DOS formula:
`a^2 - b^2 = (a + b)(a - b)`

Multiply:

• 
  `(1 + \sqrt5)(1 - \sqrt5)`
• 
  `(1^2) - (\sqrt5)^2`
• 
  `1 - 5`
• 
  `-4`

The product of the two roots is -4.