Mister Exam
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How to use it?
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Equation (x^2-4)^2+(x^2-3x-10)^2=0
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Equation 3^x=7
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Identical expressions
- x^ two -8x- eighty-four = zero
- x squared minus 8x minus 84 equally 0
- x to the power of two minus 8x minus eighty minus four equally zero
- x2-8x-84=0
- x²-8x-84=0
- x to the power of 2-8x-84=0
- x^2-8x-84=O
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Similar expressions
- x^2+8x-84=0
- x^2-8x+84=0
x^2-8x-84=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
$$a = 1$$
$$b = -8$$
$$c = -84$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 14$$
$$x_{2} = -6$$
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
$$a = 1$$
$$b = -8$$
$$c = -84$$
, then
D = b^2 - 4 * a * c =
(-8)^2 - 4 * (1) * (-84) = 400
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 14$$
$$x_{2} = -6$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = -84$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = -84$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = -84$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = -84$$
Sum and product of roots
[src]
sum
-6 + 14
$$-6 + 14$$
=
8
$$8$$
product
-6*14
$$- 84$$
=
-84
$$-84$$
-84