Mister Exam
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How to use it?
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Equation k^2+4=0
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Identical expressions
- k^ two + four = zero
- k squared plus 4 equally 0
- k to the power of two plus four equally zero
- k2+4=0
- k²+4=0
- k to the power of 2+4=0
- k^2+4=O
-
Similar expressions
- k^2-4=0
k^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:
$$k_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$k_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 0$$
$$c = 4$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$k_{1} = 2 i$$
Simplify
$$k_{2} = - 2 i$$
Simplify
a*k^2 + b*k + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$k_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$k_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 0$$
$$c = 4$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (4) = -16
Because D<0, then the equation
has no real roots,
but complex roots is exists.
k1 = (-b + sqrt(D)) / (2*a)
k2 = (-b - sqrt(D)) / (2*a)
or
$$k_{1} = 2 i$$
Simplify
$$k_{2} = - 2 i$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 4$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 0$$
$$k_{1} k_{2} = 4$$
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 4$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 0$$
$$k_{1} k_{2} = 4$$
Sum and product of roots
[src]
sum
0 - 2*I + 2*I
$$\left(0 - 2 i\right) + 2 i$$
=
0
$$0$$
product
1*-2*I*2*I
$$2 i 1 \left(- 2 i\right)$$
=
4
$$4$$
4
The graph