Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 81*x^3+18*x^2+x=0
-
Equation 6=8-5(7x-1)
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Equation (-x-4)*(3*x+3)=0
- Equation x^2-144=0
- Express {x} in terms of y where:
- -14*x-8*y=20
- -1*x+4*y=-10
- 8*x+6*y=20
- -11*x-19*y=14
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Identical expressions
- x^ two - one hundred and forty-four = zero
- x squared minus 144 equally 0
- x to the power of two minus one hundred and forty minus four equally zero
- x2-144=0
- x²-144=0
- x to the power of 2-144=0
- x^2-144=O
-
Similar expressions
- x^2+144=0
x^2-144=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
$$a = 1$$
$$b = 0$$
$$c = -144$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 12$$
$$x_{2} = -12$$
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
$$a = 1$$
$$b = 0$$
$$c = -144$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (1) * (-144) = 576
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 12$$
$$x_{2} = -12$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -144$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -144$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -144$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -144$$
Sum and product of roots
[src]
sum
-12 + 12
$$-12 + 12$$
=
0
$$0$$
product
-12*12
$$- 144$$
=
-144
$$-144$$
-144