Mister Exam
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How to use it?
- Equation:
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Equation |x|=-1
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Equation tan(x)=7
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Equation 6-3*(x+1)=7-2*x
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Identical expressions
- x^ two + six *x+ two = zero
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- x2+6*x+2=0
- x²+6*x+2=0
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- x^2+6x+2=0
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Similar expressions
- x^2-6*x+2=0
- x^2+6*x-2=0
x^2+6*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
$$a = 1$$
$$b = 6$$
$$c = 2$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -3 + \sqrt{7}$$
$$x_{2} = -3 - \sqrt{7}$$
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
$$a = 1$$
$$b = 6$$
$$c = 2$$
, then
D = b^2 - 4 * a * c =
(6)^2 - 4 * (1) * (2) = 28
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -3 + \sqrt{7}$$
$$x_{2} = -3 - \sqrt{7}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = 2$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -6$$
$$x_{1} x_{2} = 2$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 6$$
$$q = \frac{c}{a}$$
$$q = 2$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -6$$
$$x_{1} x_{2} = 2$$
Sum and product of roots
[src]
sum
___ ___ -3 - \/ 7 + -3 + \/ 7
$$\left(-3 - \sqrt{7}\right) + \left(-3 + \sqrt{7}\right)$$
=
-6
$$-6$$
product
/ ___\ / ___\ \-3 - \/ 7 /*\-3 + \/ 7 /
$$\left(-3 - \sqrt{7}\right) \left(-3 + \sqrt{7}\right)$$
=
2
$$2$$
2
Rapid solution
[src]
___ x1 = -3 - \/ 7
$$x_{1} = -3 - \sqrt{7}$$
___ x2 = -3 + \/ 7
$$x_{2} = -3 + \sqrt{7}$$
x2 = -3 + sqrt(7)
The graph