How do you solve #-3n^2 + 5n - 2= 0# using the formula?
Solve -3x^2 + 5x - 2 = 0
For this type of equation, we don't need a lengthy solving process. Use the shortcut. When (a + b + c = 0), one real root is (1) and the other is (c/a = 2/3).
Remind of Shortcut Rule.
The shortcut will save us a lot of work and effort.
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First we need to remember the formula:
("Minus b, plus or minus the square root of b squared minus 4 a c all over 2a".)
You may notice that every number I substituted is in parentheses in this first step. I think that is a good habit to develop for all formulas.
Now we have some simplification/arithmetic to do (I'll remove the colors now)
There are two solutions:
The opposite of plus or minus 1, is minus or plus 1. Which is surely the same as plus or minus 1. So
Finally, notice that when we finish the arithmetic, we get the same answers:
(We got the same numbers in the opposite order.)
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To solve the quadratic equation -3n^2 + 5n - 2 = 0 using the quadratic formula, which is (n = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}), where (a = -3), (b = 5), and (c = -2):
- Substitute the values of (a), (b), and (c) into the quadratic formula.
- Calculate the discriminant, which is (b^2 - 4ac).
- If the discriminant is positive, you will have two real solutions. If it's zero, there will be one real solution (a repeated root). If it's negative, there will be no real solutions (two complex solutions).
- Plug the values of (a), (b), and the discriminant into the quadratic formula and solve for (n).
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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