Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sqrt(x+2*sqrt(x-1))+sqrt(x-2*sqrt(x-1))=2
-
Equation k^2-2*k-3=0
- Equation ctgx=-√3
-
Equation (y^2)/(y^2-6y)=4(3-2y)/(y(6-y))
- Express {x} in terms of y where:
- -10*x+18*y=6
- 9*x-18*y=6
- -1*x+19*y=-10
- 4*x+13*y=13
-
Identical expressions
- k^ two - two *k- three = zero
- k squared minus 2 multiply by k minus 3 equally 0
- k to the power of two minus two multiply by k minus three equally zero
- k2-2*k-3=0
- k²-2*k-3=0
- k to the power of 2-2*k-3=0
- k^2-2k-3=0
- k2-2k-3=0
- k^2-2*k-3=O
-
Similar expressions
- k^2-2*k+3=0
- k^2+2*k-3=0
k^2-2*k-3=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
$$a = 1$$
$$b = -2$$
$$c = -3$$
, then
Because D > 0, then the equation has two roots.
or
$$k_{1} = 3$$
Simplify
$$k_{2} = -1$$
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
$$a = 1$$
$$b = -2$$
$$c = -3$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (-3) = 16
Because D > 0, then the equation has two roots.
k1 = (-b + sqrt(D)) / (2*a)
k2 = (-b - sqrt(D)) / (2*a)
or
$$k_{1} = 3$$
Simplify
$$k_{2} = -1$$
Simplify
Vieta's Theorem
it is reduced quadratic equation
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 2$$
$$k_{1} k_{2} = -3$$
$$k^{2} + k p + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -3$$
Vieta Formulas
$$k_{1} + k_{2} = - p$$
$$k_{1} k_{2} = q$$
$$k_{1} + k_{2} = 2$$
$$k_{1} k_{2} = -3$$
Sum and product of roots
[src]
sum
0 - 1 + 3
$$\left(-1 + 0\right) + 3$$
=
2
$$2$$
product
1*-1*3
$$1 \left(-1\right) 3$$
=
-3
$$-3$$
-3
The graph