How do you find the roots, real and imaginary, of #y= x^2-x-2 # using the quadratic formula?

Answer 1

The roots are rational (i.e. real) and are #2# and #-1#.

The quadratic formula gives the roots of the general form of quadratic equation #ax^2+bx+c=0# as #x=(-b+-sqrt(b^2-4ac))/(2a)#.
The roots of a quadratic equation thus critically depend on the discriminant #b^2-4ac#.
In #y=x^2-x-2#, the discriminant is
#(-1)^2-4×1×(-2)#
= #1+8=9#

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

#(-(-1)+-sqrt((-1)^2-4×1×(-2)))/2# or
#(1+-sqrt9)/2=(1+-3)/2#
i.e. #2# and #-1#
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Answer 2

To find the roots of (y = x^2 - x - 2) using the quadratic formula:

  1. Identify the coefficients: (a = 1), (b = -1), (c = -2).
  2. Substitute the coefficients into the quadratic formula: (x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}).
  3. Plug in the values: (x = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4(1)(-2)}}}}{{2(1)}}).
  4. Simplify: (x = \frac{{1 \pm \sqrt{{1 + 8}}}}{2}).
  5. Further simplify: (x = \frac{{1 \pm \sqrt{9}}}{2}).
  6. 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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Answer from HIX Tutor

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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