Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 3*x^2-2=0
-
Equation x+(x*3)=168
- Equation x-1=1+(1/2)*y
-
Equation -4+x/5=x+4/2
- Express {x} in terms of y where:
- 15*x+2*y=8
- 1*x+4*y=-11
- 5*x-18*y=-17
- -9*x+6*y=18
- Graphing y =:
-
2x^2-8x+30
-
Identical expressions
- two x^2-8x+ thirty = zero
- 2x squared minus 8x plus 30 equally 0
- two x squared minus 8x plus thirty equally zero
- 2x2-8x+30=0
- 2x²-8x+30=0
- 2x to the power of 2-8x+30=0
- 2x^2-8x+30=O
-
Similar expressions
- 2x^2-8x-30=0
- 2x^2+8x+30=0
2x^2-8x+30=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
$$a = 2$$
$$b = -8$$
$$c = 30$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = 2 + \sqrt{11} i$$
$$x_{2} = 2 - \sqrt{11} i$$
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
$$a = 2$$
$$b = -8$$
$$c = 30$$
, then
D = b^2 - 4 * a * c =
(-8)^2 - 4 * (2) * (30) = -176
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
$$x_{1} = 2 + \sqrt{11} i$$
$$x_{2} = 2 - \sqrt{11} i$$
Vieta's Theorem
rewrite the equation
$$\left(2 x^{2} - 8 x\right) + 30 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 4 x + 15 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = 15$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = 15$$
$$\left(2 x^{2} - 8 x\right) + 30 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 4 x + 15 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = 15$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = 15$$
Sum and product of roots
[src]
sum
____ ____ 2 - I*\/ 11 + 2 + I*\/ 11
$$\left(2 - \sqrt{11} i\right) + \left(2 + \sqrt{11} i\right)$$
=
4
$$4$$
product
/ ____\ / ____\ \2 - I*\/ 11 /*\2 + I*\/ 11 /
$$\left(2 - \sqrt{11} i\right) \left(2 + \sqrt{11} i\right)$$
=
15
$$15$$
15
Rapid solution
[src]
____ x1 = 2 - I*\/ 11
$$x_{1} = 2 - \sqrt{11} i$$
____ x2 = 2 + I*\/ 11
$$x_{2} = 2 + \sqrt{11} i$$
x2 = 2 + sqrt(11)*i
Numerical answer
[src]
x1 = 2.0 + 3.3166247903554*i
x2 = 2.0 - 3.3166247903554*i
x2 = 2.0 - 3.3166247903554*i