How do you use the quadratic formula to find both solutions to the quadratic equation #5 - 10x - 3x^2 = 0#?
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To find both solutions to the quadratic equation (5 - 10x - 3x^2 = 0), you can use the quadratic formula, which is:
[x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}]
In the given equation, (a = -3), (b = -10), and (c = 5).
Substitute these values into the quadratic formula and solve for (x):
[x = \frac{{-(-10) \pm \sqrt{{(-10)^2 - 4(-3)(5)}}}}{{2(-3)}}] [x = \frac{{10 \pm \sqrt{{100 + 60}}}}{{-6}}] [x = \frac{{10 \pm \sqrt{{160}}}}{{-6}}] [x = \frac{{10 \pm 4\sqrt{{10}}i}}{{-6}}]
So the solutions are:
[x_1 = \frac{{10 + 4\sqrt{{10}}i}}{{-6}}]
[x_2 = \frac{{10 - 4\sqrt{{10}}i}}{{-6}}]
Where (i) is the imaginary unit.
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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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