Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -7x=4
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Equation x^2-6=0
- Equation x^2-x-90=0
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Equation x^2+7*x+12=0
- Express {x} in terms of y where:
- -6*x-11*y=-20
- -15*x+7*y=1
- -1*x-20*y=1
- -1*x-15*y=13
- Factor squared:
- x^2+4*x+2
-
Identical expressions
- x^ two + four *x+ two = zero
- x squared plus 4 multiply by x plus 2 equally 0
- x to the power of two plus four multiply by x plus two equally zero
- x2+4*x+2=0
- x²+4*x+2=0
- x to the power of 2+4*x+2=0
- x^2+4x+2=0
- x2+4x+2=0
- x^2+4*x+2=O
-
Similar expressions
- x^2+4*x-2=0
- x^2-4*x+2=0
x^2+4*x+2=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
$$a = 1$$
$$b = 4$$
$$c = 2$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -2 + \sqrt{2}$$
$$x_{2} = -2 - \sqrt{2}$$
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
$$a = 1$$
$$b = 4$$
$$c = 2$$
, then
D = b^2 - 4 * a * c =
(4)^2 - 4 * (1) * (2) = 8
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -2 + \sqrt{2}$$
$$x_{2} = -2 - \sqrt{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = 2$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = 2$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = 2$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = 2$$
Sum and product of roots
[src]
sum
___ ___ -2 - \/ 2 + -2 + \/ 2
$$\left(-2 - \sqrt{2}\right) + \left(-2 + \sqrt{2}\right)$$
=
-4
$$-4$$
product
/ ___\ / ___\ \-2 - \/ 2 /*\-2 + \/ 2 /
$$\left(-2 - \sqrt{2}\right) \left(-2 + \sqrt{2}\right)$$
=
2
$$2$$
2
Rapid solution
[src]
___ x1 = -2 - \/ 2
$$x_{1} = -2 - \sqrt{2}$$
___ x2 = -2 + \/ 2
$$x_{2} = -2 + \sqrt{2}$$
x2 = -2 + sqrt(2)
The graph