Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 2*x^2-x-1=x^2-5*x-(-1-x^2)
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Equation e^x=0
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Equation 9*(x-5)=-x
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Equation x^2+2x-3=0
- Express {x} in terms of y where:
- 10*x-2*y=0
- 4*x-1*y=-3
- 2*x+1*y=-8
- 2*x+2*y=-6
- Derivative of:
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x^2+2x-3
- Integral of d{x}:
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x^2+2x-3
- Canonical form:
- x^2+2x-3
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Identical expressions
- x^ two +2x- three = zero
- x squared plus 2x minus 3 equally 0
- x to the power of two plus 2x minus three equally zero
- x2+2x-3=0
- x²+2x-3=0
- x to the power of 2+2x-3=0
- x^2+2x-3=O
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Similar expressions
- x^2+2x+3=0
- x^2-2x-3=0
x^2+2x-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
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 2$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -2$$
$$x_{1} x_{2} = -3$$
$$p x + q + x^{2} = 0$$
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