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- Equação:
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Equação x^4-x^3+5*x^2=0
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Equação cos(x)=sin(x)
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Equação sqrt(x-1)=x
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Equação 3x^2+6x=0
- Express {x} in terms of y where:
- 17*x-19*y=1
- 10*x+9*y=-4
- -12*x+3*y=-9
- 9*x-18*y=6
- Derivative of:
- x^2-x-20
- Graphing y =:
- x^2-x-20
- Factor polynomial:
- x^2-x-20
-
Identical expressions
- x^ two -x- twenty = zero
- x squared minus x minus 20 equally 0
- x to the power of two minus x minus twenty equally zero
- x2-x-20=0
- x²-x-20=0
- x to the power of 2-x-20=0
- x^2-x-20=O
-
Similar expressions
- x^2+x-20=0
- x^2-x+20=0
x^2-x-20=0 equação
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A solução
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
$$a = 1$$
$$b = -1$$
$$c = -20$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 5$$
$$x_{2} = -4$$
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
$$a = 1$$
$$b = -1$$
$$c = -20$$
, then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (1) * (-20) = 81
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 5$$
$$x_{2} = -4$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -20$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = -20$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -20$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = -20$$
Sum and product of roots
[src]
sum
-4 + 5
$$-4 + 5$$
=
1
$$1$$
product
-4*5
$$- 20$$
=
-20
$$-20$$
-20
Gráfico