Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2+3x=0
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Equation x-6/2-x/3=3
- Equation (x+20)*(-x+10)=0
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Equation 0,2x+2,7=1,4-1,1x
- Express {x} in terms of y where:
- -17*x-15*y=-17
- -2*x+7*y=-14
- -1*x+6*y=-20
- -11*x+10*y=-3
- Graphing y =:
- -x^2+2*x+3
- Derivative of:
-
-x^2+2*x+3
- Factor polynomial:
- -x^2+2*x+3
-
Identical expressions
- -x^ two + two *x+ three = zero
- minus x squared plus 2 multiply by x plus 3 equally 0
- minus x to the power of two plus two multiply by x plus three equally zero
- -x2+2*x+3=0
- -x²+2*x+3=0
- -x to the power of 2+2*x+3=0
- -x^2+2x+3=0
- -x2+2x+3=0
- -x^2+2*x+3=O
-
Similar expressions
- -x^2-2*x+3=0
- -x^2+2*x-3=0
- x^2+2*x+3=0
-x^2+2*x+3=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
$$a = -1$$
$$b = 2$$
$$c = 3$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -1$$
$$x_{2} = 3$$
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
$$a = -1$$
$$b = 2$$
$$c = 3$$
, then
D = b^2 - 4 * a * c =
(2)^2 - 4 * (-1) * (3) = 16
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -1$$
$$x_{2} = 3$$
Vieta's Theorem
rewrite the equation
$$\left(- x^{2} + 2 x\right) + 3 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 2 x - 3 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -3$$
$$\left(- x^{2} + 2 x\right) + 3 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 2 x - 3 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -3$$
The graph