Pregunta
What are the solutions to the equation?
and
and
and
Ask by George Cruz. in the United States
Mar 11,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
Responder
The solutions to the equation are
and
.
Solución
We start by checking the two candidate pairs of solutions. When we have a quadratic with two roots
and
, we know that (up to a nonzero constant multiple) the equation can be written in factored form as
Two things to verify are the sum and product of the roots.
If the two roots are
and
, then by Vieta’s formulas for a quadratic
(with
) we have:
Let’s compare the candidate answer options:
-
If the proposed solutions arethen
-
If the proposed solutions arethen
-
If the proposed solutions arethen
Without the original equation explicitly given, one common scenario is that the quadratic’s coefficients are such that the factored form (after clearing fractions) is
Expanding this gives:
Here the sum and product of the roots are:
which exactly match the values from option 2.
Thus, the solutions to the equation are
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Extra Insights
To solve for the values of
in an equation, we typically set it to zero and factor it. If you’ve narrowed down the solutions as potential pairs, it might be helpful to substitute these values back into the original equation to check if they indeed satisfy it. Testing all options can help clear up any confusion!
When working with equations that produce quadratic or linear results, remember to remember the signs and how they affect the answers. A common mistake is overlooking negative signs or miscalculating the roots. Always double-check each solution to see if it holds true in the original equation!

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