Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation x+y=5
-
Equation x^2+5x+6=0
-
Equation tan(x)=-1/2
-
Equation 1*(x-1)*(x-3)=0
- Express {x} in terms of y where:
- -2*x-19*y=3
- -18*x-14*y=12
- -9*x+1*y=3
- 4*x+18*y=-7
- Graphing y =:
-
x^2+2x
- Derivative of:
-
x^2+2x
- Integral of d{x}:
-
x^2+2x
-
Identical expressions
- x^ two +2x
- x squared plus 2x
- x to the power of two plus 2x
- x2+2x
- x²+2x
- x to the power of 2+2x
-
Similar expressions
- x^2-2x
x^2+2x 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
$$a = 1$$
$$b = 2$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
Simplify
$$x_{2} = -2$$
Simplify
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
$$a = 1$$
$$b = 2$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(2)^2 - 4 * (1) * (0) = 4
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
Simplify
$$x_{2} = -2$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = 0$$
Sum and product of roots
[src]
sum
0 - 2 + 0
$$\left(-2 + 0\right) + 0$$
=
-2
$$-2$$
product
1*-2*0
$$1 \left(-2\right) 0$$
=
0
$$0$$
0
The graph