Mister Exam
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- Equation:
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Equation (x+3)^4-4(x+3)^2-5=0
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Equation x^2+14*x+24=0
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Equation (x+3)^4+2(x+3)^2-8=0
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Identical expressions
- x^ two + fourteen *x+ twenty-four = zero
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- x to the power of two plus fourteen multiply by x plus twenty minus four equally zero
- x2+14*x+24=0
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Similar expressions
- x^2-14*x+24=0
- x^2+14*x-24=0
x^2+14*x+24=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
$$a = 1$$
$$b = 14$$
$$c = 24$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -2$$
$$x_{2} = -12$$
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
$$a = 1$$
$$b = 14$$
$$c = 24$$
, then
D = b^2 - 4 * a * c =
(14)^2 - 4 * (1) * (24) = 100
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -2$$
$$x_{2} = -12$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 14$$
$$q = \frac{c}{a}$$
$$q = 24$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -14$$
$$x_{1} x_{2} = 24$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 14$$
$$q = \frac{c}{a}$$
$$q = 24$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -14$$
$$x_{1} x_{2} = 24$$
Sum and product of roots
[src]
sum
-12 - 2
$$-12 - 2$$
=
-14
$$-14$$
product
-12*(-2)
$$- -24$$
=
24
$$24$$
24
The graph