How do you find the roots of #x^2-6x+12=0#?
Given: Consider Now lets look at the equation part : As this is negative the graph does not have any x-intercepts where There will be a solution of But
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
By signing up, you agree to our Terms of Service and Privacy Policy
To find the roots of (x^2 - 6x + 12 = 0), you can use the quadratic formula, which is (x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}), where (a), (b), and (c) are the coefficients of the quadratic equation. For this equation, (a = 1), (b = -6), and (c = 12). Substituting these values into the quadratic formula:
[x = \frac{{-(-6) \pm \sqrt{{(-6)^2 - 4 \cdot 1 \cdot 12}}}}{{2 \cdot 1}}]
[x = \frac{{6 \pm \sqrt{{36 - 48}}}}{2}]
[x = \frac{{6 \pm \sqrt{{-12}}}}{2}]
Since the square root of -12 is imaginary, the roots are complex. Therefore, the roots are:
[x = \frac{{6 + \sqrt{{-12}}}}{2} = \frac{{6 + 2i\sqrt{3}}}{2} = 3 + i\sqrt{3}]
[x = \frac{{6 - \sqrt{{-12}}}}{2} = \frac{{6 - 2i\sqrt{3}}}{2} = 3 - i\sqrt{3}]
By signing up, you agree to our Terms of Service and Privacy Policy
You can use the quadratic formula to find the roots of the equation (x^2 - 6x + 12 = 0).
The quadratic formula is: (x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}), where (a), (b), and (c) are the coefficients of the quadratic equation (ax^2 + bx + c = 0).
For the given equation (x^2 - 6x + 12 = 0):
- (a = 1),
- (b = -6),
- (c = 12).
Substituting these values into the quadratic formula:
(x = \frac{{-(-6) \pm \sqrt{{(-6)^2 - 4 \cdot 1 \cdot 12}}}}{{2 \cdot 1}})
(x = \frac{{6 \pm \sqrt{{36 - 48}}}}{2})
(x = \frac{{6 \pm \sqrt{{-12}}}}{2})
Since the discriminant (b^2 - 4ac) is negative, the roots will be complex numbers.
(x = \frac{{6 \pm \sqrt{{-12}}}}{2})
(x = \frac{{6 \pm 2i\sqrt{3}}}{2})
(x = 3 \pm i\sqrt{3})
So, the roots of the equation (x^2 - 6x + 12 = 0) are (3 + i\sqrt{3}) and (3 - i\sqrt{3}).
By signing up, you agree to our Terms of Service and Privacy Policy
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.

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7