Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sin(2*x)=-1/2
-
Equation x+(7-2x)=10
-
Equation x-2=-3x
-
Equation (x-1)*(x+1)=0
- Express {x} in terms of y where:
- -10*x+7*y=-12
- -15*x+3*y=8
- 18*x-10*y=-9
- 19*x-7*y=-11
- Graphing y =:
- 2x^2-3x+2
-
Identical expressions
- two x^ two -3x+2= zero
- 2x squared minus 3x plus 2 equally 0
- two x to the power of two minus 3x plus 2 equally zero
- 2x2-3x+2=0
- 2x²-3x+2=0
- 2x to the power of 2-3x+2=0
- 2x^2-3x+2=O
-
Similar expressions
- 2x^2+3x+2=0
- 2x^2-3x-2=0
2x^2-3x+2=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
$$a = 2$$
$$b = -3$$
$$c = 2$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \frac{3}{4} + \frac{\sqrt{7} i}{4}$$
$$x_{2} = \frac{3}{4} - \frac{\sqrt{7} i}{4}$$
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
$$a = 2$$
$$b = -3$$
$$c = 2$$
, then
D = b^2 - 4 * a * c =
(-3)^2 - 4 * (2) * (2) = -7
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{3}{4} + \frac{\sqrt{7} i}{4}$$
$$x_{2} = \frac{3}{4} - \frac{\sqrt{7} i}{4}$$
Vieta's Theorem
rewrite the equation
$$\left(2 x^{2} - 3 x\right) + 2 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{3 x}{2} + 1 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{3}{2}$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{3}{2}$$
$$x_{1} x_{2} = 1$$
$$\left(2 x^{2} - 3 x\right) + 2 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - \frac{3 x}{2} + 1 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = - \frac{3}{2}$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = \frac{3}{2}$$
$$x_{1} x_{2} = 1$$
Sum and product of roots
[src]
sum
___ ___ 3 I*\/ 7 3 I*\/ 7 - - ------- + - + ------- 4 4 4 4
$$\left(\frac{3}{4} - \frac{\sqrt{7} i}{4}\right) + \left(\frac{3}{4} + \frac{\sqrt{7} i}{4}\right)$$
=
3/2
$$\frac{3}{2}$$
product
/ ___\ / ___\ |3 I*\/ 7 | |3 I*\/ 7 | |- - -------|*|- + -------| \4 4 / \4 4 /
$$\left(\frac{3}{4} - \frac{\sqrt{7} i}{4}\right) \left(\frac{3}{4} + \frac{\sqrt{7} i}{4}\right)$$
=
1
$$1$$
1
Rapid solution
[src]
___
3 I*\/ 7
x1 = - - -------
4 4
$$x_{1} = \frac{3}{4} - \frac{\sqrt{7} i}{4}$$
___
3 I*\/ 7
x2 = - + -------
4 4
$$x_{2} = \frac{3}{4} + \frac{\sqrt{7} i}{4}$$
x2 = 3/4 + sqrt(7)*i/4
Numerical answer
[src]
x1 = 0.75 - 0.661437827766148*i
x2 = 0.75 + 0.661437827766148*i
x2 = 0.75 + 0.661437827766148*i
The graph