Mister Exam
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How to use it?
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Identical expressions
- x^ two -4x- twenty-seven = zero
- x squared minus 4x minus 27 equally 0
- x to the power of two minus 4x minus twenty minus seven equally zero
- x2-4x-27=0
- x²-4x-27=0
- x to the power of 2-4x-27=0
- x^2-4x-27=O
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Similar expressions
- x^2-4x+27=0
- x^2+4x-27=0
x^2-4x-27=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
$$a = 1$$
$$b = -4$$
$$c = -27$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2 + \sqrt{31}$$
$$x_{2} = 2 - \sqrt{31}$$
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
$$a = 1$$
$$b = -4$$
$$c = -27$$
, then
D = b^2 - 4 * a * c =
(-4)^2 - 4 * (1) * (-27) = 124
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2 + \sqrt{31}$$
$$x_{2} = 2 - \sqrt{31}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = -27$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = -27$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -4$$
$$q = \frac{c}{a}$$
$$q = -27$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 4$$
$$x_{1} x_{2} = -27$$
Rapid solution
[src]
____ x1 = 2 - \/ 31
$$x_{1} = 2 - \sqrt{31}$$
____ x2 = 2 + \/ 31
$$x_{2} = 2 + \sqrt{31}$$
x2 = 2 + sqrt(31)
Sum and product of roots
[src]
sum
____ ____ 2 - \/ 31 + 2 + \/ 31
$$\left(2 - \sqrt{31}\right) + \left(2 + \sqrt{31}\right)$$
=
4
$$4$$
product
/ ____\ / ____\ \2 - \/ 31 /*\2 + \/ 31 /
$$\left(2 - \sqrt{31}\right) \left(2 + \sqrt{31}\right)$$
=
-27
$$-27$$
-27