Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2=5
-
Equation k^2+k=0
-
Equation 5x=0
-
Equation x^2-15=2x
- Express {x} in terms of y where:
- -4*x+3*y=9
- -2*x-19*y=-11
- -5*x+15*y=-15
- -1*x+7*y=-11
- Sum of series:
-
k^2+k
-
Identical expressions
- k^ two +k= zero
- k squared plus k equally 0
- k to the power of two plus k equally zero
- k2+k=0
- k²+k=0
- k to the power of 2+k=0
- k^2+k=O
-
Similar expressions
- k^2-k=0
k^2+k=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
$$a = 1$$
$$b = 1$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$k_{1} = 0$$
$$k_{2} = -1$$
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
$$a = 1$$
$$b = 1$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (1) * (0) = 1
Because D > 0, then the equation has two roots.
k1 = (-b + sqrt(D)) / (2*a)
k2 = (-b - sqrt(D)) / (2*a)
or
$$k_{1} = 0$$
$$k_{2} = -1$$
Vieta's Theorem
it is reduced quadratic equation
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = -1$$
$$k_{1} k_{2} = 0$$
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 1$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = -1$$
$$k_{1} k_{2} = 0$$
The graph