What is this as a slope?
1 answer:
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I believe you are referring to the half-life formula, which is used to calculate the half-life (when the substance drops to half of its original amount) of radioactive substances. The equation is as follows: 
<em>A</em> is the remaining amount
<em>P</em> is the initial amount
<em>t</em> is the time that has passed
<em>h</em> is the half-life of the substance
When plugging values into the equation, make sure that <em>t </em>and <em>h </em>are both measured in the same unit (e.g. <em>t </em>days and <em>h </em>days), as well as <em>A </em>and <em>P</em>.
<em>A</em> is the remaining amount
<em>P</em> is the initial amount
<em>t</em> is the time that has passed
<em>h</em> is the half-life of the substance
When plugging values into the equation, make sure that <em>t </em>and <em>h </em>are both measured in the same unit (e.g. <em>t </em>days and <em>h </em>days), as well as <em>A </em>and <em>P</em>.
If the roots to such a polynomial are 2 and 
, then we can write it as
courtesy of the fundamental theorem of algebra. Now expanding yields
which would be the correct answer, but clearly this option is not listed. Which is silly, because none of the offered solutions are *the* polynomial of lowest degree and leading coefficient 1.
So this makes me think you're expected to increase the multiplicity of one of the given roots, or you're expected to pull another root out of thin air. Judging by the choices, I think it's the latter, and that you're somehow supposed to know to use
as a root. In this case, that would make our polynomial
so that the answer is (probably) the third choice.
Whoever originally wrote this question should reevaluate their word choice...
courtesy of the fundamental theorem of algebra. Now expanding yields
which would be the correct answer, but clearly this option is not listed. Which is silly, because none of the offered solutions are *the* polynomial of lowest degree and leading coefficient 1.
So this makes me think you're expected to increase the multiplicity of one of the given roots, or you're expected to pull another root out of thin air. Judging by the choices, I think it's the latter, and that you're somehow supposed to know to use
so that the answer is (probably) the third choice.
Whoever originally wrote this question should reevaluate their word choice...