Mister Exam
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- nine *x^ two + four = zero
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Similar expressions
- 9*x^2-4=0
9*x^2+4=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
$$a = 9$$
$$b = 0$$
$$c = 4$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = \frac{2 i}{3}$$
$$x_{2} = - \frac{2 i}{3}$$
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
$$a = 9$$
$$b = 0$$
$$c = 4$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (9) * (4) = -144
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
$$x_{1} = \frac{2 i}{3}$$
$$x_{2} = - \frac{2 i}{3}$$
Vieta's Theorem
rewrite the equation
$$9 x^{2} + 4 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{4}{9} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{4}{9}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = \frac{4}{9}$$
$$9 x^{2} + 4 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{4}{9} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = \frac{4}{9}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = \frac{4}{9}$$
Rapid solution
[src]
-2*I
x1 = ----
3
$$x_{1} = - \frac{2 i}{3}$$
2*I
x2 = ---
3
$$x_{2} = \frac{2 i}{3}$$
x2 = 2*i/3
Sum and product of roots
[src]
sum
2*I 2*I - --- + --- 3 3
$$- \frac{2 i}{3} + \frac{2 i}{3}$$
=
0
$$0$$
product
-2*I 2*I ----*--- 3 3
$$- \frac{2 i}{3} \frac{2 i}{3}$$
=
4/9
$$\frac{4}{9}$$
4/9