MHB Do 1 + √5 and 1 - √5 Solve the Equation x² - 2x - 4 = 0?

[mathdad]

Verify that the numbers 1 + √5 and 1 - √5 both satisfy the equation x^2 - 2x - 4 = 0.

I believe the question is asking to plug the given numbers into the quadratic equation and evaluate individually.

Let x = 1 + √5 and evaluate.

Let x = 1 - √5 and evaluate.

Both numbers should yield 0 = 0.

If the result for each number given is 0 = 0, then we can say that 1 + √5 and 1 - √5 are solutions of the quadratic equation.

Is this right?

 

[MarkFL]

In my opinion, your method is valid, but I also think that solving the equation however you choose and showing the resulting roots are equivalent to the given roots is also a way to verify that they satisfy the equation. :D

View attachment 6634

(Evilgrin) (Giggle)(Smoking)(Tongueout)

 

[Opalg]

Another approach is to say that the numbers $1+\sqrt5$ and $1-\sqrt5$ have sum $2$ and product $-4$, and so they are the solutions of the equation $x^2 - 2x - 4 = 0.$

 

[mathdad]

This question is more evaluation practice more than anything else.