Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x/4+x=-5
-
Equation x^4-13x^2+36=0
-
Equation x^4=(2x-3)^2
-
Equation -x=14
- Express {x} in terms of y where:
- -10*x-2*y=18
- -10*x-12*y=-10
- 8*x+1*y=4
- 20*x-16*y=7
-
Identical expressions
- x^ two -2x+ ten = zero
- x squared minus 2x plus 10 equally 0
- x to the power of two minus 2x plus ten equally zero
- x2-2x+10=0
- x²-2x+10=0
- x to the power of 2-2x+10=0
- x^2-2x+10=O
-
Similar expressions
- x^2+2x+10=0
- x^2-2x-10=0
x^2-2x+10=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
$$a = 1$$
$$b = -2$$
$$c = 10$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = 1 + 3 i$$
$$x_{2} = 1 - 3 i$$
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
$$a = 1$$
$$b = -2$$
$$c = 10$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (10) = -36
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
$$x_{1} = 1 + 3 i$$
$$x_{2} = 1 - 3 i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = 10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = 10$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = 10$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = 10$$
Sum and product of roots
[src]
sum
1 - 3*I + 1 + 3*I
$$\left(1 - 3 i\right) + \left(1 + 3 i\right)$$
=
2
$$2$$
product
(1 - 3*I)*(1 + 3*I)
$$\left(1 - 3 i\right) \left(1 + 3 i\right)$$
=
10
$$10$$
10
The graph