Question 695911
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Find the product of the solutions of this equation. 3x^2 - 12x + 7 = 0.
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This is a nice question,  and it has a nice answer.


To get the product of the roots of this equation,  you do not need to solve the equation 
and you do not need to find the roots explicitly,  as the other tutor makes in his post.


Instead,  use the  Vieta's theorem.


It says that the product of the roots of a quadratic equation   ax^2 + bx + c = 0


is always   {{{c/a}}},   or the constant term divided by the leading coefficient at  x^2.



In your case,  the product of the roots is    {{{7/3}}},    so you get the answer instantly,  without making long calculations.



The  Vieta's theorem works for real roots and for complex roots:  in other words,  it works for any quadratic equation.


It is  UNIVERSAL.



This problem is specially given to you to check if you are familiar with the  Vieta's theorem,

and if you are not familiar with it,  it is a good chance to learn it and to see how perfectly it works.



It is also a good question for an interview, since it allows to learn momentarily,
if a person knows Algebra and generally a school Math uniformly.
How a person answers this question, it demonstrates/reflects the person's mathematical culture.