Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^4+2*x^2-8=0
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Equation x^2-2x+1=0
-
Equation x^4+4=0
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Equation 3(x+3)=2x+5
- Express {x} in terms of y where:
- 2*x+13*y=19
- -17*x+18*y=10
- 7*x-1*y=-7
- 10*x-18*y=3
- Derivative of:
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x^2-2x+1
- Integral of d{x}:
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x^2-2x+1
- Canonical form:
- x^2-2x+1
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Identical expressions
- x^ two -2x+ one = zero
- x squared minus 2x plus 1 equally 0
- x to the power of two minus 2x plus one equally zero
- x2-2x+1=0
- x²-2x+1=0
- x to the power of 2-2x+1=0
- x^2-2x+1=O
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Similar expressions
- x^2+2x+1=0
- x^2-2x-1=0
x^2-2x+1=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
$$a = 1$$
$$b = -2$$
$$c = 1$$
, 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
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = 1$$
The graph