Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 6-5(4x-1)=3
-
Equation (x-2)(-2x-3)=0
-
Equation x+5=7
-
Equation |3|x|-5|=-2x-2
- Express {x} in terms of y where:
- 8*x-4*y=10
- -6*x-11*y=-20
- -15*x+7*y=1
- -10*x+4*y=3
- Derivative of:
-
2*x^2+x
- Graphing y =:
- 2*x^2+x
- Integral of d{x}:
- 2*x^2+x
-
Identical expressions
- two *x^ two +x= zero
- 2 multiply by x squared plus x equally 0
- two multiply by x to the power of two plus x equally zero
- 2*x2+x=0
- 2*x²+x=0
- 2*x to the power of 2+x=0
- 2x^2+x=0
- 2x2+x=0
- 2*x^2+x=O
-
Similar expressions
- 2*x^2-x=0
2*x^2+x=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
$$a = 2$$
$$b = 1$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = - \frac{1}{2}$$
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
$$a = 2$$
$$b = 1$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (2) * (0) = 1
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = - \frac{1}{2}$$
Vieta's Theorem
rewrite the equation
$$2 x^{2} + x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{x}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{1}{2}$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{1}{2}$$
$$x_{1} x_{2} = 0$$
$$2 x^{2} + x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{x}{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{1}{2}$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{1}{2}$$
$$x_{1} x_{2} = 0$$
Sum and product of roots
[src]
sum
-1/2
$$- \frac{1}{2}$$
=
-1/2
$$- \frac{1}{2}$$
product
0*(-1) ------ 2
$$\frac{\left(-1\right) 0}{2}$$
=
0
$$0$$
0
The graph