Mister Exam
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How to use it?
- Equation:
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Equation 4x-x^2=x^2-x+3
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Equation (x-4)/x=(2*x+10)/(x+4)
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Equation -2(x+5)+3=2-3(x+1)
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Equation 2*x^2+2*x-12=0
- Express {x} in terms of y where:
- -8*x+10*y=19
- -5*x+3*y=10
- -14*x+6*y=7
- -5*x+19*y=-1
- Graphing y =:
- 9*x^2+1
-
Identical expressions
- nine *x^ two + one = zero
- 9 multiply by x squared plus 1 equally 0
- nine multiply by x to the power of two plus one equally zero
- 9*x2+1=0
- 9*x²+1=0
- 9*x to the power of 2+1=0
- 9x^2+1=0
- 9x2+1=0
- 9*x^2+1=O
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Similar expressions
- 9*x^2-1=0
9*x^2+1=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
$$a = 9$$
$$b = 0$$
$$c = 1$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \frac{i}{3}$$
$$x_{2} = - \frac{i}{3}$$
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
$$a = 9$$
$$b = 0$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (9) * (1) = -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
$$x_{1} = \frac{i}{3}$$
$$x_{2} = - \frac{i}{3}$$
Vieta's Theorem
rewrite the equation
$$9 x^{2} + 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{1}{9} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{1}{9}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = \frac{1}{9}$$
$$9 x^{2} + 1 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{1}{9} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{1}{9}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = \frac{1}{9}$$
Rapid solution
[src]
-I
x1 = ---
3
$$x_{1} = - \frac{i}{3}$$
I
x2 = -
3
$$x_{2} = \frac{i}{3}$$
x2 = i/3
Sum and product of roots
[src]
sum
I I - - + - 3 3
$$- \frac{i}{3} + \frac{i}{3}$$
=
0
$$0$$
product
-I I ---*- 3 3
$$- \frac{i}{3} \frac{i}{3}$$
=
1/9
$$\frac{1}{9}$$
1/9
The graph