Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 4-6*(x+2)=3-5*x
-
Equation 1/(x-3)^2-3/(x-3)-4=0
-
Equation x^2-2x+1=0
-
Equation 3(x+3)=2x+5
- Express {x} in terms of y where:
- 2*x+13*y=19
- 17*x-20*y=6
- 5*x-13*y=17
- -9*x-1*y=6
- Derivative of:
-
x²+2x+1
-
Identical expressions
- x²+2x+ one
- x² plus 2x plus 1
- x² plus 2x plus one
-
Similar expressions
- x²+2x-1
- (x²+2x)+1=0
- x²-2x+1
x²+2x+1 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
$$a = 1$$
$$b = 2$$
$$c = 1$$
, then
Because D = 0, then the equation has one root.
$$x_{1} = -1$$
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
$$a = 1$$
$$b = 2$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(2)^2 - 4 * (1) * (1) = 0
Because D = 0, then the equation has one root.
x = -b/2a = -2/2/(1)
$$x_{1} = -1$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = 1$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = 1$$