Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x-5)/2=2*(3x/7-1/2)/3
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Equation (x^2-4)^2+(x^2-3*x-10)^2=0
-
Equation cos(x)+sin(x)=0
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Equation 7+x=4
- Express {x} in terms of y where:
- 7*x-2*y=20
- -7*x-7*y=-14
- -15*x+17*y=13
- 20*x+4*y=-7
- Integral of d{x}:
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x^2-3
- Canonical form:
- x^2-3
- Derivative of:
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x^2-3
-
Identical expressions
- x^ two - three = zero
- x squared minus 3 equally 0
- x to the power of two minus three equally zero
- x2-3=0
- x²-3=0
- x to the power of 2-3=0
- x^2-3=O
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Similar expressions
- x^2+3=0
- 6x^4+23x^3+3x^2-32x+12=0
- (x^2-x-20)(x^2-3x-18)=252
- sqrt(16-x^2)*(x^2-3*x-10)=0
x^2-3=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
$$a = 1$$
$$b = 0$$
$$c = -3$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{3}$$
Simplify
$$x_{2} = - \sqrt{3}$$
Simplify
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
$$a = 1$$
$$b = 0$$
$$c = -3$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-3) = 12
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{3}$$
Simplify
$$x_{2} = - \sqrt{3}$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -3$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -3$$
Sum and product of roots
[src]
sum
___ ___ 0 - \/ 3 + \/ 3
$$\left(- \sqrt{3} + 0\right) + \sqrt{3}$$
=
0
$$0$$
product
___ ___ 1*-\/ 3 *\/ 3
$$\sqrt{3} \cdot 1 \left(- \sqrt{3}\right)$$
=
-3
$$-3$$
-3
The graph