Mister Exam
Other calculators
-
How to use it?
- Equation:
- Equation a*x=b
-
Equation x^2-x+8=0
-
Equation 2^x=7
-
Equation 3x^2-2x=0
- Express {x} in terms of y where:
- 2*x+19*y=-7
- -4*x+7*y=-16
- -16*x+3*y=17
- 12*x-20*y=9
- Graphing y =:
- 3x^2-2x
- Derivative of:
-
3x^2-2x
- Integral of d{x}:
- 3x^2-2x
-
Identical expressions
- 3x^ two -2x= zero
- 3x squared minus 2x equally 0
- 3x to the power of two minus 2x equally zero
- 3x2-2x=0
- 3x²-2x=0
- 3x to the power of 2-2x=0
- 3x^2-2x=O
-
Similar expressions
- 3x^2+2x=0
3x^2-2x=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
$$a = 3$$
$$b = -2$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{2}{3}$$
$$x_{2} = 0$$
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
$$a = 3$$
$$b = -2$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (3) * (0) = 4
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{2}{3}$$
$$x_{2} = 0$$
Vieta's Theorem
rewrite the equation
$$3 x^{2} - 2 x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{2 x}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{2}{3}$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{2}{3}$$
$$x_{1} x_{2} = 0$$
$$3 x^{2} - 2 x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{2 x}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{2}{3}$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{2}{3}$$
$$x_{1} x_{2} = 0$$
Sum and product of roots
[src]
sum
2/3
$$\frac{2}{3}$$
=
2/3
$$\frac{2}{3}$$
product
0*2 --- 3
$$\frac{0 \cdot 2}{3}$$
=
0
$$0$$
0
The graph