Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2+x=12
-
Equation 3x-2(3x-2)=19
-
Equation x^4=(x-56)^2
-
Equation (-2x+1)*(-2x-7)=0
- Express {x} in terms of y where:
- -7*x-13*y=-12
- 8*x+1*y=4
- 20*x-16*y=7
- -3*x+19*y=16
- Derivative of:
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x^2-2x-5
- Integral of d{x}:
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x^2-2x-5
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Identical expressions
- x^ two -2x- five = zero
- x squared minus 2x minus 5 equally 0
- x to the power of two minus 2x minus five equally zero
- x2-2x-5=0
- x²-2x-5=0
- x to the power of 2-2x-5=0
- x^2-2x-5=O
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Similar expressions
- x^2-2x+5=0
- x^2+2x-5=0
x^2-2x-5=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
$$a = 1$$
$$b = -2$$
$$c = -5$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 1 + \sqrt{6}$$
$$x_{2} = 1 - \sqrt{6}$$
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
$$a = 1$$
$$b = -2$$
$$c = -5$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (-5) = 24
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 1 + \sqrt{6}$$
$$x_{2} = 1 - \sqrt{6}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -5$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -5$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -5$$
Rapid solution
[src]
___ x1 = 1 - \/ 6
$$x_{1} = 1 - \sqrt{6}$$
___ x2 = 1 + \/ 6
$$x_{2} = 1 + \sqrt{6}$$
x2 = 1 + sqrt(6)
Sum and product of roots
[src]
sum
___ ___ 1 - \/ 6 + 1 + \/ 6
$$\left(1 - \sqrt{6}\right) + \left(1 + \sqrt{6}\right)$$
=
2
$$2$$
product
/ ___\ / ___\ \1 - \/ 6 /*\1 + \/ 6 /
$$\left(1 - \sqrt{6}\right) \left(1 + \sqrt{6}\right)$$
=
-5
$$-5$$
-5
The graph