Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation (x+3)^2=4
-
Equation 9*(x-1)=x+15
-
Equation x*x-x+7=0
-
Equation 5*sqrt(x-3)=-2
- Express {x} in terms of y where:
- -1*x+11*y=-9
- 1*x+18*y=-5
- 5*x+20*y=-4
- -11*x+9*y=8
- Graphing y =:
- x^2+4*x+8
- Factor squared:
- x^2+4*x+8
- Factor polynomial:
- x^2+4*x+8
-
Identical expressions
- x^ two + four *x+ eight = zero
- x squared plus 4 multiply by x plus 8 equally 0
- x to the power of two plus four multiply by x plus eight equally zero
- x2+4*x+8=0
- x²+4*x+8=0
- x to the power of 2+4*x+8=0
- x^2+4x+8=0
- x2+4x+8=0
- x^2+4*x+8=O
-
Similar expressions
- x^2-4*x+8=0
- x^2+4*x-8=0
x^2+4*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
$$a = 1$$
$$b = 4$$
$$c = 8$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = -2 + 2 i$$
$$x_{2} = -2 - 2 i$$
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
$$a = 1$$
$$b = 4$$
$$c = 8$$
, then
D = b^2 - 4 * a * c =
(4)^2 - 4 * (1) * (8) = -16
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -2 + 2 i$$
$$x_{2} = -2 - 2 i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = 8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = 8$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = 8$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = 8$$
Rapid solution
[src]
x1 = -2 - 2*I
$$x_{1} = -2 - 2 i$$
x2 = -2 + 2*I
$$x_{2} = -2 + 2 i$$
x2 = -2 + 2*i
Sum and product of roots
[src]
sum
-2 - 2*I + -2 + 2*I
$$\left(-2 - 2 i\right) + \left(-2 + 2 i\right)$$
=
-4
$$-4$$
product
(-2 - 2*I)*(-2 + 2*I)
$$\left(-2 - 2 i\right) \left(-2 + 2 i\right)$$
=
8
$$8$$
8
The graph