Quadratics: Factoring and Solving Quadratics Using FOIL
In the equation $$x^2+14x+k=0$$, $$x$$ is a variable, and $$k$$ is a constant. If $$x−1$$ is a factor of the equation $$x^2+14x+k=0$$, then which of the following is a solution of $$x^2+14x+k=0$$?
Alternative method:
Remember: the solution for a quadratic equation of the form $$ax^2+bx+c=0$$ is the value of $$x$$ for which the quadratic equals 0.
If $$x-1$$ is a factor of the quadratic, then setting the factor to 0 will yield $$x=1$$ as a solution of the quadratic. Plug in $$x=1$$ into the equation to find $$k$$, then factor the equation to find the other root.
Incorrect.
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Answer choice E is the value of $$f$$, the other factor of the quadratic. However, the question asked for the solution of the equation.
Incorrect.
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Check your work.
Incorrect.
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You might have gotten this answer if you used $$e=1$$, instead of $$e=-1$$.
Incorrect.
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Carefully check your calculations.
Correct.
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For the quadratic $$x^2+14x+k=0$$, you know that $$a=1$$, $$b=14$$, and $$c=k$$.
The sum of $${e}$$ and $${f}$$ must be equal to $${b=14}$$. If $${e}=-1$$ is one of the values of the factors, then $$-1+{f}=14$$, or $$f=15$$.
Plug in $${e}$$ and $${f}$$ into the expanded form of the quadratic:
>$$(x-{1})(x+{15})=0$$.
Then set the factors equal to 0 to find the solutions:
> $$x+15=0$$
> $$x=-15$$
-15
-14
-13
13
15
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