Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x+2)/9=(x-3)/2
-
Equation 11+2x=55+3x
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Equation (x-2)^4+3*(x-2)^2-10=0
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Equation 3*x^2-18=0
- Express {x} in terms of y where:
- 2*x+3*y=14
- 18*x-8*y=-2
- 16*x-7*y=-5
- 10*x-16*y=-6
- Graphing y =:
- 3*x^2-18
- Derivative of:
-
3*x^2-18
-
Identical expressions
- three *x^ two - eighteen = zero
- 3 multiply by x squared minus 18 equally 0
- three multiply by x to the power of two minus eighteen equally zero
- 3*x2-18=0
- 3*x²-18=0
- 3*x to the power of 2-18=0
- 3x^2-18=0
- 3x2-18=0
- 3*x^2-18=O
-
Similar expressions
- 3*x^2+18=0
3*x^2-18=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
$$a = 3$$
$$b = 0$$
$$c = -18$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \sqrt{6}$$
Simplify
$$x_{2} = - \sqrt{6}$$
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
$$a = 3$$
$$b = 0$$
$$c = -18$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (3) * (-18) = 216
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \sqrt{6}$$
Simplify
$$x_{2} = - \sqrt{6}$$
Simplify
Vieta's Theorem
rewrite the equation
$$3 x^{2} - 18 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 6 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -6$$
$$3 x^{2} - 18 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 6 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -6$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -6$$
Sum and product of roots
[src]
sum
___ ___ 0 - \/ 6 + \/ 6
$$\left(- \sqrt{6} + 0\right) + \sqrt{6}$$
=
0
$$0$$
product
___ ___ 1*-\/ 6 *\/ 6
$$\sqrt{6} \cdot 1 \left(- \sqrt{6}\right)$$
=
-6
$$-6$$
-6
The graph