Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 5*sin(x)+cos(x)=5
-
Equation 4*x^2+7=7+24*x
-
Equation 2x^2-3x-2=0
-
Equation x^2-7*x+10=0
- Express {x} in terms of y where:
- 17*x-19*y=-12
- 3*x+19*y=4
- 13*x-1*y=-20
- -16*x-9*y=-1
- Graphing y =:
- x^2-6*x+2
- Derivative of:
- x^2-6*x+2
-
Identical expressions
- x^ two - six *x+ two = zero
- x squared minus 6 multiply by x plus 2 equally 0
- x to the power of two minus six multiply by x plus two equally zero
- x2-6*x+2=0
- x²-6*x+2=0
- x to the power of 2-6*x+2=0
- x^2-6x+2=0
- x2-6x+2=0
- x^2-6*x+2=O
-
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
$$x_{1} = \sqrt{7} + 3$$
$$x_{2} = 3 - \sqrt{7}$$
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
$$x_{1} = \sqrt{7} + 3$$
$$x_{2} = 3 - \sqrt{7}$$
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
$$\left(3 - \sqrt{7}\right) + \left(\sqrt{7} + 3\right)$$
=
6
$$6$$
product
/ ___\ / ___\ \3 - \/ 7 /*\3 + \/ 7 /
$$\left(3 - \sqrt{7}\right) \left(\sqrt{7} + 3\right)$$
=
2
$$2$$
2
Rapid solution
[src]
___ x1 = 3 - \/ 7
$$x_{1} = 3 - \sqrt{7}$$
___ x2 = 3 + \/ 7
$$x_{2} = \sqrt{7} + 3$$
x2 = sqrt(7) + 3
The graph