Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 4+8x-5x^2=0
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Equation x+(8-3x)=12
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Equation (x^2+5x)/(x(x-2))=(6)/(x(x-2))
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Equation 3*x-4/6=7/8
- Express {x} in terms of y where:
- 16*x+14*y=-14
- 11*x-15*y=3
- 9*x-1*y=-2
- -13*x-15*y=9
- Integral of d{x}:
- -x^2+3*x
- Factor polynomial:
- -x^2+3*x
- Limit of the function:
-
-x^2+3*x
-
Identical expressions
- -x^ two + three *x= zero
- minus x squared plus 3 multiply by x equally 0
- minus x to the power of two plus three multiply by x equally zero
- -x2+3*x=0
- -x²+3*x=0
- -x to the power of 2+3*x=0
- -x^2+3x=0
- -x2+3x=0
- -x^2+3*x=O
-
Similar expressions
- -x^2-3*x=0
- x^2+3*x=0
-x^2+3*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
$$a = -1$$
$$b = 3$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = 3$$
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
$$a = -1$$
$$b = 3$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(3)^2 - 4 * (-1) * (0) = 9
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = 3$$
Vieta's Theorem
rewrite the equation
$$- x^{2} + 3 x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 3 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 3$$
$$x_{1} x_{2} = 0$$
$$- x^{2} + 3 x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 3 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -3$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 3$$
$$x_{1} x_{2} = 0$$
The graph