Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x+10)^2=(x-9)^2
- Equation k^2+1=0
-
Equation k^2-2*k+5=0
- Equation 4x^2-100=0
- Express {x} in terms of y where:
- 14*x-16*y=14
- -12*x+3*y=-9
- 9*x-18*y=6
- -10*x+18*y=6
-
Identical expressions
- k^ two + one = zero
- k squared plus 1 equally 0
- k to the power of two plus one equally zero
- k2+1=0
- k²+1=0
- k to the power of 2+1=0
- k^2+1=O
-
Similar expressions
- k^2-1=0
k^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:
$$k_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$k_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = 0$$
$$c = 1$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$k_{1} = i$$
Simplify
$$k_{2} = - i$$
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
$$a = 1$$
$$b = 0$$
$$c = 1$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (1) = -4
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
$$k_{1} = i$$
Simplify
$$k_{2} = - i$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 0$$
$$k_{1} k_{2} = 1$$
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = 1$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 0$$
$$k_{1} k_{2} = 1$$
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