Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x-5)/2=2*(3x/7-1/2)/3
-
Equation x^4-4*x^3-2*x^2+12*x+9=0
-
Equation sin(x)=-1
-
Equation cos(x)=sqrt(3)/2
- Express {x} in terms of y where:
- 18*x-20*y=-7
- 1*x-6*y=-19
- -19*x-14*y=-8
- 9*x-4*y=2
- Integral of d{x}:
- 3*x^2+3
-
Identical expressions
- three *x^ two + three = zero
- 3 multiply by x squared plus 3 equally 0
- three multiply by x to the power of two plus three equally zero
- 3*x2+3=0
- 3*x²+3=0
- 3*x to the power of 2+3=0
- 3x^2+3=0
- 3x2+3=0
- 3*x^2+3=O
-
Similar expressions
- 3*x^2-3=0
3*x^2+3=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
$$a = 3$$
$$b = 0$$
$$c = 3$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = i$$
Simplify
$$x_{2} = - i$$
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
$$a = 3$$
$$b = 0$$
$$c = 3$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (3) * (3) = -36
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
$$x_{1} = i$$
Simplify
$$x_{2} = - i$$
Simplify
Vieta's Theorem
rewrite the equation
$$3 x^{2} + 3 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + 1 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 1$$
$$3 x^{2} + 3 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + 1 = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = 1$$
Sum and product of roots
[src]
sum
0 - I + I
$$\left(0 - i\right) + i$$
=
0
$$0$$
product
1*-I*I
$$i 1 \left(- i\right)$$
=
1
$$1$$
1
The graph