SOLUTION: Hello, I need to write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax^2 + bx + c = 0. The given numbers a

Question 400987: Hello,
I need to write a quadratic equation in the variable x having the given numbers as solutions. Type the equation in standard form, ax^2 + bx + c = 0. The given numbers are two solutions: - sqrt 3, index 3 sqrt 3.
I am not sure how to type the the index number, sorry. What I know is initially it looks like:
. I am not sure how to make this into a quadratic equation. Could you show me in complete detail how to do this please? Thank you :)
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
I think by "index 3 sqrt 3" you mean . If this is correct, then it is called the cube root of 3. It is not a square root of any kind.

Your expression:

is correct. But we need an equation, not an expression. The equation is simply

Now we just need it in form. For this we just multiply out the left side using FOIL:

What follows will make more sense if we rewrite the equation as additions. (Also, the form is written as additions.):

Factoring out x from the middle two terms we get:

If you have not yet learned about fractional exponents then the equation above is your answer with...
"a" being 1
"b" being
and "c" being

If you do know about fractional exponents then we can simplify . Rewriting this with fractional exponents we get:

The rule for exponents when multiplying is to add the exponents. These exponents are fractions and to add fractions we need a common denominator:

Now we can multiply:

We can now write this back in radical form:

so this becomes:

This makes our full, simplified equation:

and ...
"a" being 1
"b" being
and "c" being

(Note: The "b", , cannot be simplified, even if you use fractional exponents. They are not like terms and cannot be transformed into like terms. So we can never add them.)
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