Mister Exam
Other calculators
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How to use it?
- Equation:
-
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
- Factor squared:
- x^2+4*x+9
- Canonical form:
- x^2+4*x+9
-
Identical expressions
- x^ two + four *x+ nine = zero
- x squared plus 4 multiply by x plus 9 equally 0
- x to the power of two plus four multiply by x plus nine equally zero
- x2+4*x+9=0
- x²+4*x+9=0
- x to the power of 2+4*x+9=0
- x^2+4x+9=0
- x2+4x+9=0
- x^2+4*x+9=O
-
Similar expressions
- x^2-4*x+9=0
- x^2+4*x-9=0
x^2+4*x+9=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
$$a = 1$$
$$b = 4$$
$$c = 9$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = -2 + \sqrt{5} i$$
$$x_{2} = -2 - \sqrt{5} i$$
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
$$a = 1$$
$$b = 4$$
$$c = 9$$
, then
D = b^2 - 4 * a * c =
(4)^2 - 4 * (1) * (9) = -20
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
$$x_{1} = -2 + \sqrt{5} i$$
$$x_{2} = -2 - \sqrt{5} i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = 9$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = 9$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = 9$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = 9$$
Rapid solution
[src]
___ x1 = -2 - I*\/ 5
$$x_{1} = -2 - \sqrt{5} i$$
___ x2 = -2 + I*\/ 5
$$x_{2} = -2 + \sqrt{5} i$$
x2 = -2 + sqrt(5)*i
Sum and product of roots
[src]
sum
___ ___ -2 - I*\/ 5 + -2 + I*\/ 5
$$\left(-2 - \sqrt{5} i\right) + \left(-2 + \sqrt{5} i\right)$$
=
-4
$$-4$$
product
/ ___\ / ___\ \-2 - I*\/ 5 /*\-2 + I*\/ 5 /
$$\left(-2 - \sqrt{5} i\right) \left(-2 + \sqrt{5} i\right)$$
=
9
$$9$$
9
Numerical answer
[src]
x1 = -2.0 - 2.23606797749979*i
x2 = -2.0 + 2.23606797749979*i
x2 = -2.0 + 2.23606797749979*i
The graph