How do you find the roots, real and imaginary, of #y= x^2-x-2 # using the quadratic formula?
The roots are rational (i.e. real) and are
As it is a complete square one can easily take square root and roots of equation will be rational (i.e. real).
The roots are
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To find the roots of (y = x^2 - x - 2) using the quadratic formula:
- Identify the coefficients: (a = 1), (b = -1), (c = -2).
- Substitute the coefficients into the quadratic formula: (x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}).
- Plug in the values: (x = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4(1)(-2)}}}}{{2(1)}}).
- Simplify: (x = \frac{{1 \pm \sqrt{{1 + 8}}}}{2}).
- Further simplify: (x = \frac{{1 \pm \sqrt{9}}}{2}).
- Calculate the roots: (x_1 = \frac{{1 + 3}}{2} = 2), (x_2 = \frac{{1 - 3}}{2} = -1).
So, the real roots are (x = 2) and (x = -1), while there are no imaginary roots.
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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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