Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation tan(x)=7
-
Equation x^3-3x^2+4=0
-
Equation x^4-9*x^2+20=0
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Equation x^2+2x+10=0
- Express {x} in terms of y where:
- -17*x+6*y=14
- -18*x-8*y=-18
- 12*x+11*y=20
- 17*x+14*y=-17
- Integral of d{x}:
-
x^2+2x+10
-
Identical expressions
- x^ two +2x+ ten = zero
- x squared plus 2x plus 10 equally 0
- x to the power of two plus 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
Rapid solution
[src]
x1 = -1 - 3*I
$$x_{1} = -1 - 3 i$$
x2 = -1 + 3*I
$$x_{2} = -1 + 3 i$$
x2 = -1 + 3*i
The graph