Mister Exam
Other calculators
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How to use it?
- Equation:
- Equation k^2+1=0
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Equation x^4-7x^2+12=0
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Equation tgx=-1
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Equation x^2-2x-24=0
- Express {x} in terms of y where:
- 4*x-16*y=6
- 10*x-1*y=10
- 15*x-17*y=19
- sqrt(x^2+y^2+4x-6y-12)+(x^2+10x-27)=8-|y-9|+|y-3|
- Graphing y =:
- x^2-2x-24
-
Identical expressions
- x^ two -2x- twenty-four = zero
- x squared minus 2x minus 24 equally 0
- x to the power of two minus 2x minus twenty minus four equally zero
- x2-2x-24=0
- x²-2x-24=0
- x to the power of 2-2x-24=0
- x^2-2x-24=O
-
Similar expressions
- x^2+2x-24=0
- x^2-2x+24=0
x^2-2x-24=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
$$a = 1$$
$$b = -2$$
$$c = -24$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 6$$
$$x_{2} = -4$$
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
$$a = 1$$
$$b = -2$$
$$c = -24$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (-24) = 100
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 6$$
$$x_{2} = -4$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -24$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -24$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -24$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -24$$
Sum and product of roots
[src]
sum
-4 + 6
$$-4 + 6$$
=
2
$$2$$
product
-4*6
$$- 24$$
=
-24
$$-24$$
-24
The graph