Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 1+sin(x)=0
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Equation tg(x)=1
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Equation -x-4+5(x+3)=5(-1-x)-2
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Equation 49,86-(0.3+0.049*49,86)=x
- Express {x} in terms of y where:
- 4*x+2*y=5
- 1*x+10*y=-18
- -18*x-2*y=9
- -11*x+9*y=-20
- Graphing y =:
- -x^2+x
- Factor polynomial:
- -x^2+x
- Integral of d{x}:
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-x^2+x
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Identical expressions
- -x^ two +x= zero
- minus x squared plus x equally 0
- minus x to the power of two plus x equally zero
- -x2+x=0
- -x²+x=0
- -x to the power of 2+x=0
- -x^2+x=O
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Similar expressions
- x^2+x=0
- -x^2-x=0
-x^2+x=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
$$a = -1$$
$$b = 1$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = 1$$
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
$$a = -1$$
$$b = 1$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (-1) * (0) = 1
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = 1$$
Vieta's Theorem
rewrite the equation
$$- x^{2} + x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = 0$$
$$- x^{2} + x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = 0$$
The graph