Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation -24-y=-16
-
Equation 4(x-6)=x-9
-
Equation x*(x^2+8*x+16)=5*(x+4)
-
Equation -x^2+4x+3=x^2-x-(1+2x^2)
- Express {x} in terms of y where:
- 10*x-15*y=16
- -18*x-6*y=-1
- -6*x-10*y=19
- -1*x-17*y=-12
- Graphing y =:
- x^2-8*x+12
- Factor polynomial:
- x^2-8*x+12
- Factor squared:
- x^2-8*x+12
-
Identical expressions
- x^ two - eight *x+ twelve = zero
- x squared minus 8 multiply by x plus 12 equally 0
- x to the power of two minus eight multiply by x plus twelve equally zero
- x2-8*x+12=0
- x²-8*x+12=0
- x to the power of 2-8*x+12=0
- x^2-8x+12=0
- x2-8x+12=0
- x^2-8*x+12=O
-
Similar expressions
- x^2+8*x+12=0
- x^2-8*x-12=0
x^2-8*x+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
$$a = 1$$
$$b = -8$$
$$c = 12$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 6$$
$$x_{2} = 2$$
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
$$a = 1$$
$$b = -8$$
$$c = 12$$
, then
D = b^2 - 4 * a * c =
(-8)^2 - 4 * (1) * (12) = 16
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 6$$
$$x_{2} = 2$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = 12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = 12$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = 12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = 12$$
Sum and product of roots
[src]
sum
2 + 6
$$2 + 6$$
=
8
$$8$$
product
2*6
$$2 \cdot 6$$
=
12
$$12$$
12
The graph