Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 4x-x^2=x^2-x+3
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Equation x^6=-64
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Equation x^2-21=4x
- Equation x+y=12
- Express {x} in terms of y where:
- 12*x+6*y=-5
- -19*x+1*y=-6
- 2*x+4*y=-1
- 4*x-20*y=1
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Identical expressions
- x^ two + sixty-nine *x+ one thousand and eighty = zero
- x squared plus 69 multiply by x plus 1080 equally 0
- x to the power of two plus sixty minus nine multiply by x plus one thousand and eighty equally zero
- x2+69*x+1080=0
- x²+69*x+1080=0
- x to the power of 2+69*x+1080=0
- x^2+69x+1080=0
- x2+69x+1080=0
- x^2+69*x+1080=O
-
Similar expressions
- x^2-69*x+1080=0
- x^2+69*x-1080=0
x^2+69*x+1080=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
$$a = 1$$
$$b = 69$$
$$c = 1080$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -24$$
$$x_{2} = -45$$
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
$$a = 1$$
$$b = 69$$
$$c = 1080$$
, then
D = b^2 - 4 * a * c =
(69)^2 - 4 * (1) * (1080) = 441
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -24$$
$$x_{2} = -45$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 69$$
$$q = \frac{c}{a}$$
$$q = 1080$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -69$$
$$x_{1} x_{2} = 1080$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 69$$
$$q = \frac{c}{a}$$
$$q = 1080$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -69$$
$$x_{1} x_{2} = 1080$$
Sum and product of roots
[src]
sum
-45 - 24
$$-45 - 24$$
=
-69
$$-69$$
product
-45*(-24)
$$- -1080$$
=
1080
$$1080$$
1080