Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2+3x+2=0
- Equation x+y=5
-
Equation sin(x)=3
-
Equation x^2-11*x+30=0
- Express {x} in terms of y where:
- 6*x+17*y=-11
- -13*x+7*y=-15
- -14*x-8*y=20
- 9*x+14*y=-10
- Graphing y =:
- x^2+6*x+8
- Derivative of:
- x^2+6*x+8
- Factor polynomial:
- x^2+6*x+8
-
Identical expressions
- x^ two + six *x+ eight = zero
- x squared plus 6 multiply by x plus 8 equally 0
- x to the power of two plus six multiply by x plus eight equally zero
- x2+6*x+8=0
- x²+6*x+8=0
- x to the power of 2+6*x+8=0
- x^2+6x+8=0
- x2+6x+8=0
- x^2+6*x+8=O
-
Similar expressions
- x^2-6*x+8=0
- x^2+6*x-8=0
x^2+6*x+8=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
$$a = 1$$
$$b = 6$$
$$c = 8$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -2$$
$$x_{2} = -4$$
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
$$a = 1$$
$$b = 6$$
$$c = 8$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (1) * (8) = 4
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -2$$
$$x_{2} = -4$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = 8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -6$$
$$x_{1} x_{2} = 8$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = 8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -6$$
$$x_{1} x_{2} = 8$$
Sum and product of roots
[src]
sum
-4 - 2
$$-4 - 2$$
=
-6
$$-6$$
product
-4*(-2)
$$- -8$$
=
8
$$8$$
8
The graph