Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation sin(x)+cos(x)=-1
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Equation √(x^2-1)^3=2*x
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Equation sin(x)+sin(2*x)+sin(3*x)=0
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Equation sqrt(x-1)=3-x
- Express {x} in terms of y where:
- 12*x+14*y=-15
- 4*x-7*y=4
- -10*x-18*y=6
- -11*x+10*y=-9
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Identical expressions
- x^ two - two *x- eighty = zero
- x squared minus 2 multiply by x minus 80 equally 0
- x to the power of two minus two multiply by x minus eighty equally zero
- x2-2*x-80=0
- x²-2*x-80=0
- x to the power of 2-2*x-80=0
- x^2-2x-80=0
- x2-2x-80=0
- x^2-2*x-80=O
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Similar expressions
- x^2+2*x-80=0
- x^2-2*x+80=0
x^2-2*x-80=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
$$a = 1$$
$$b = -2$$
$$c = -80$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 10$$
$$x_{2} = -8$$
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
$$a = 1$$
$$b = -2$$
$$c = -80$$
, then
D = b^2 - 4 * a * c =
(-2)^2 - 4 * (1) * (-80) = 324
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 10$$
$$x_{2} = -8$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -80$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -80$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -2$$
$$q = \frac{c}{a}$$
$$q = -80$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 2$$
$$x_{1} x_{2} = -80$$
Sum and product of roots
[src]
sum
-8 + 10
$$-8 + 10$$
=
2
$$2$$
product
-8*10
$$- 80$$
=
-80
$$-80$$
-80