Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation tgx=-1
-
Equation 2x^2-7x+6=0
-
Equation 2sin^2x+sinx-1=0
-
Equation 8x^2=0
- Express {x} in terms of y where:
- 10*x-1*y=10
- 15*x-17*y=19
- 9*x-8*y=6
- 15*x+15*y=16
-
Identical expressions
- x^ two +999x− one thousand = zero .
- x squared plus 999x−1000 equally 0.
- x to the power of two plus 999x− one thousand equally zero .
- x2+999x−1000=0.
- x²+999x−1000=0.
- x to the power of 2+999x−1000=0.
- x^2+999x−1000=O.
-
Similar expressions
- x^2-999x−1000=0.
x^2+999x−1000=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
$$a = 1$$
$$b = 999$$
$$c = -1000$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 1$$
$$x_{2} = -1000$$
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
$$a = 1$$
$$b = 999$$
$$c = -1000$$
, then
D = b^2 - 4 * a * c =
(999)^2 - 4 * (1) * (-1000) = 1002001
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 1$$
$$x_{2} = -1000$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 999$$
$$q = \frac{c}{a}$$
$$q = -1000$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -999$$
$$x_{1} x_{2} = -1000$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 999$$
$$q = \frac{c}{a}$$
$$q = -1000$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -999$$
$$x_{1} x_{2} = -1000$$
Sum and product of roots
[src]
sum
-1000 + 1
$$-1000 + 1$$
=
-999
$$-999$$
product
-1000
$$-1000$$
=
-1000
$$-1000$$
-1000