Question 1190033: Did I get the correct answer on finding the quadratic equation when having the given roots below:
Given roots (-3, 1) - I come up with equation x^2 + 2x - 3 = 0 - Is this correct equation?
Also, could you show me step by step how to obtain equations for the 2 known roots below:
Known Roots = (1/5, 1/2) - steps to find equation on this one.
Known Roots = (1 + Radicand 2, 1 - Radicand 2) - steps to find equation on this one.
Thank you
Answer by ikleyn(52778)   (Show Source):
You can put this solution on YOUR website! .
Hello, there is simple and direct way to check if the given number is the root to given equation.
This way is to substitute the value unto equation and calculate.
Next, if you are given two values -3 and 1, then there are TWO WAYS to construct a quadratic equation with the given roots.
First way is to take two associated binomials (x-(-3)) = (x+3) and (x-1) and multiply these binomials.
So, your quadratic equation will be
(x+3)*(x-1) = 0.
If you want to have left side in the standard form, make FOIL.
Second way is to use Vieta's theorem.
It says that the sough equation has the leading coefficient 1 (one) at x^2;
the coefficient at x is the sum of the supposed roots with the opposite sign;
and the constant term is the product of the supposed roots.
So, in your case, the leading coefficient is 1; the coefficient at x is -((-3) + 1) = - (-2) = 2 and the constant term is (-3)*1 = -3.
Thus the quadratic polynomial is x^2 + 2x - 3 (exactly, as your polynomial).
So, I wrote a lot at this post, and it is just time for me to STOP.
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