Write this set implicitly and explicitly: S1S_{1} is the set of the zero points of f(x)=x2−2x−6f(x)=x^{2}-2x-6

Write this set implicitly and explicitly: S1S_{1} is the set of the
zero points of the quadratic polynomial f(x)=x2−2x−6f(x)=x^{2}-2x-6

This is the task but the problem is, I don’t know what’s meant by “implicit” and “explicit”..
For sure one of both is, calculate the zero points and then all zero points correspond to one of both sets (either explicit or implicit) but which one? And how to write the other one?

So f(x)=0f(x)= 0

0=x2−2x−60=x^{2}-2x-6

x1,2=22+−√(−22)2+6x_{1,2}=\frac{2}{2}+-\sqrt{\left(-\frac{2}{2}\right)^{2}+6}

x1,2=1+−√7x_{1,2}=1+-\sqrt{7}

x1=1+√7x_{1}=1+\sqrt{7}

x2=1−√7x_{2}=1-\sqrt{7}

I believe this will be the explicit set?

So explicit set S1={1+√7;1−√7}S_{1}=\left\{1+\sqrt{7};1-\sqrt{7}\right\}

I hope this is correct for the explicit set?

Well, what is the implicit then?

Just S1={x∈R|x2−2x−6=0}S_{1}=\left\{x \in \mathbb{R}|x^{2}-2x-6=0\right\}?

Please tell m because there are like 10 tasks of this and if I don’t understand the principle I will do all wrong : /

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Explicitly and implicitly have no standard meaning. I would interpret them the way you did here. The question ought to be more clearly stated.
– Ken Duna
2 days ago

  

 

That’s all I wrote here, about the description. What I kept away: You may not use a calculator and we are supposed to draw some of the sets too… I’m really hoping for some more comments, thank you for this one 🙂
– cnmesr
2 days ago

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Yes, cnmesr, I think you interpreted., and answered, the question correctly.
– amWhy
2 days ago

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