Mister Exam
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How to use it?
- Equation:
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Equation sin(x)=0
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Equation 2*x^2+18*x=0
- Equation x^2+18*x-19=0
- Express {x} in terms of y where:
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Identical expressions
- x^ two + eighteen *x- nineteen = zero
- x squared plus 18 multiply by x minus 19 equally 0
- x to the power of two plus eighteen multiply by x minus nineteen equally zero
- x2+18*x-19=0
- x²+18*x-19=0
- x to the power of 2+18*x-19=0
- x^2+18x-19=0
- x2+18x-19=0
- x^2+18*x-19=O
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Similar expressions
- x^2-18*x-19=0
- x^2+18*x+19=0
x^2+18*x-19=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
$$a = 1$$
$$b = 18$$
$$c = -19$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 1$$
$$x_{2} = -19$$
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
$$a = 1$$
$$b = 18$$
$$c = -19$$
, then
D = b^2 - 4 * a * c =
(18)^2 - 4 * (1) * (-19) = 400
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 1$$
$$x_{2} = -19$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 18$$
$$q = \frac{c}{a}$$
$$q = -19$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -18$$
$$x_{1} x_{2} = -19$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 18$$
$$q = \frac{c}{a}$$
$$q = -19$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -18$$
$$x_{1} x_{2} = -19$$
Sum and product of roots
[src]
sum
-19 + 1
$$-19 + 1$$
=
-18
$$-18$$
product
-19
$$-19$$
=
-19
$$-19$$
-19