Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2+9=(x+9)^2
-
Equation -x=4-3(3x-8)
-
Equation 9x-7=6x+14
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Equation x+3=-9*x
- Express {x} in terms of y where:
- -18*x-1*y=-11
- 1*x-6*y=-19
- -1*x-20*y=-17
- -13*x+7*y=11
- Derivative of:
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3*x^2-3
- Factor polynomial:
- 3*x^2-3
- Graphing y =:
- 3*x^2-3
-
Identical expressions
- three *x^ two - three = zero
- 3 multiply by x squared minus 3 equally 0
- three multiply by x to the power of two minus three equally zero
- 3*x2-3=0
- 3*x²-3=0
- 3*x to the power of 2-3=0
- 3x^2-3=0
- 3x2-3=0
- 3*x^2-3=O
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Similar expressions
- 6x^4+23x^3+3x^2-32x+12=0
- 3*x^2+3=0
3*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
$$a = 3$$
$$b = 0$$
$$c = -3$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 1$$
$$x_{2} = -1$$
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
$$a = 3$$
$$b = 0$$
$$c = -3$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (3) * (-3) = 36
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 1$$
$$x_{2} = -1$$
Vieta's Theorem
rewrite the equation
$$3 x^{2} - 3 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 1 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -1$$
$$3 x^{2} - 3 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 1 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -1$$
The graph