Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 1/(x-3)^2-3/(x-3)-4=0
-
Equation x^4+2*x^2-8=0
-
Equation (x-2)^5+(4-x)^5=2
-
Equation 6/(x+5)=-5
- Express {x} in terms of y where:
- 17*x-20*y=6
- 5*x-13*y=17
- 6*x+17*y=3
- 1*x+4*y=20
- Graphing y =:
- -x^2+x
- Factor polynomial:
- -x^2+x
- Integral of d{x}:
-
-x^2+x
-
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
-
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