Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2-8x+12=0
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Equation 3*x^2-9=0
- Equation x^4-35*x^2-36=0
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Equation x^3=64
- Express {x} in terms of y where:
- 7*x-2*y=18
- 18*x+19*y=7
- -16*x-12*y=12
- -17*x-12*y=-9
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Identical expressions
- three *x^ two - nine = zero
- 3 multiply by x squared minus 9 equally 0
- three multiply by x to the power of two minus nine equally zero
- 3*x2-9=0
- 3*x²-9=0
- 3*x to the power of 2-9=0
- 3x^2-9=0
- 3x2-9=0
- 3*x^2-9=O
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Similar expressions
- 3*x^2+9=0
3*x^2-9=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
$$a = 3$$
$$b = 0$$
$$c = -9$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{3}$$
$$x_{2} = - \sqrt{3}$$
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
$$a = 3$$
$$b = 0$$
$$c = -9$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (3) * (-9) = 108
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{3}$$
$$x_{2} = - \sqrt{3}$$
Vieta's Theorem
rewrite the equation
$$3 x^{2} - 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 3 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -3$$
$$3 x^{2} - 9 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 3 = 0$$
$$p x + q + x^{2} = 0$$
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
___ ___ - \/ 3 + \/ 3
$$- \sqrt{3} + \sqrt{3}$$
=
0
$$0$$
product
___ ___ -\/ 3 *\/ 3
$$- \sqrt{3} \sqrt{3}$$
=
-3
$$-3$$
-3
Rapid solution
[src]
___ x1 = -\/ 3
$$x_{1} = - \sqrt{3}$$
___ x2 = \/ 3
$$x_{2} = \sqrt{3}$$
x2 = sqrt(3)
The graph