Mister Exam
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Identical expressions
- x^ two +5x- twelve = zero
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Similar expressions
- x^2+5x+12=0
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x^2+5x-12=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
$$a = 1$$
$$b = 5$$
$$c = -12$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{5}{2} + \frac{\sqrt{73}}{2}$$
$$x_{2} = - \frac{\sqrt{73}}{2} - \frac{5}{2}$$
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
$$a = 1$$
$$b = 5$$
$$c = -12$$
, then
D = b^2 - 4 * a * c =
(5)^2 - 4 * (1) * (-12) = 73
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{5}{2} + \frac{\sqrt{73}}{2}$$
$$x_{2} = - \frac{\sqrt{73}}{2} - \frac{5}{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 5$$
$$q = \frac{c}{a}$$
$$q = -12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -5$$
$$x_{1} x_{2} = -12$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 5$$
$$q = \frac{c}{a}$$
$$q = -12$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -5$$
$$x_{1} x_{2} = -12$$
Rapid solution
[src]
____
5 \/ 73
x1 = - - + ------
2 2
$$x_{1} = - \frac{5}{2} + \frac{\sqrt{73}}{2}$$
____
5 \/ 73
x2 = - - - ------
2 2
$$x_{2} = - \frac{\sqrt{73}}{2} - \frac{5}{2}$$
x2 = -sqrt(73)/2 - 5/2
Sum and product of roots
[src]
sum
____ ____ 5 \/ 73 5 \/ 73 - - + ------ + - - - ------ 2 2 2 2
$$\left(- \frac{\sqrt{73}}{2} - \frac{5}{2}\right) + \left(- \frac{5}{2} + \frac{\sqrt{73}}{2}\right)$$
=
-5
$$-5$$
product
/ ____\ / ____\ | 5 \/ 73 | | 5 \/ 73 | |- - + ------|*|- - - ------| \ 2 2 / \ 2 2 /
$$\left(- \frac{5}{2} + \frac{\sqrt{73}}{2}\right) \left(- \frac{\sqrt{73}}{2} - \frac{5}{2}\right)$$
=
-12
$$-12$$
-12
The graph