Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 4(x-1)=2(2x-8)+12
-
Equation x/4+x=12
-
Equation 5^x=6-x
-
Equation 3*x=0
- Express {x} in terms of y where:
- -16*x-9*y=-1
- 4*x+13*y=8
- 14*x+17*y=19
- 3*x-11*y=20
- Graphing y =:
- x^2+4x-12
- Canonical form:
- x^2+4x-12
-
Identical expressions
- x^ two +4x- twelve = zero
- x squared plus 4x minus 12 equally 0
- x to the power of two plus 4x minus twelve equally zero
- x2+4x-12=0
- x²+4x-12=0
- x to the power of 2+4x-12=0
- x^2+4x-12=O
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Similar expressions
- x^2+4x+12=0
- x^2-4x-12=0
x^2+4x-12=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 4$$
$$c = -12$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = -6$$
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 4$$
$$c = -12$$
, then
D = b^2 - 4 * a * c =
(4)^2 - 4 * (1) * (-12) = 64
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = -6$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = -12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = -12$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = -12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = -12$$
Sum and product of roots
[src]
sum
-6 + 2
$$-6 + 2$$
=
-4
$$-4$$
product
-6*2
$$- 12$$
=
-12
$$-12$$
-12
The graph