Jung-Soon has $25 to spend on prizes for a game at the school fair. Lip balm costs $1.25 each, and
1 answer:
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Answer:
6.33... and 0.333...
Step-by-step explanation:
The quadratic formula is
.
It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions. Using the formula will require less work than finding the factors if factorable. We will substitute a=9, b=-54 and c=-19.
We will now solve for the plus and the minus.
The plus,,,
and the minus...
Now, recall Descartes Rule of Signs. Check the picture below.
the +x part, gives us the positive Real zeros, and it depends on how many times the sign changes from term to term, notice in the picture, it changed 3 times, so the positive real ones are 3, or 3-2, namely 1, so 3 or 1.
the negative real ones, come from using -x as the argument on f(x), and as you can see in the picture, there was only 1 sign change, meaning the negative real zeros are only 1.
since, based on the fundamental theorem of algebra the polynomial has 4 roots at most then,
3 positive real ones, and 1 negative real one, no complex ones
or
1 positive real one, and 1 negative real one, and 2 complex ones
bear in mind that complex always come in pairs, never alone.
the +x part, gives us the positive Real zeros, and it depends on how many times the sign changes from term to term, notice in the picture, it changed 3 times, so the positive real ones are 3, or 3-2, namely 1, so 3 or 1.
the negative real ones, come from using -x as the argument on f(x), and as you can see in the picture, there was only 1 sign change, meaning the negative real zeros are only 1.
since, based on the fundamental theorem of algebra the polynomial has 4 roots at most then,
3 positive real ones, and 1 negative real one, no complex ones
or
1 positive real one, and 1 negative real one, and 2 complex ones
bear in mind that complex always come in pairs, never alone.