Mister Exam
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How to use it?
- Equation:
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- Equation x^2-10*x-24=0
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Identical expressions
- x^ two -24x– fifty-six = zero
- x squared minus 24x–56 equally 0
- x to the power of two minus 24x– fifty minus six equally zero
- x2-24x–56=0
- x²-24x–56=0
- x to the power of 2-24x–56=0
- x^2-24x–56=O
-
Similar expressions
- x^2+24x–56=0
x^2-24x–56=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
$$a = 1$$
$$b = -24$$
$$c = -56$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 12 + 10 \sqrt{2}$$
$$x_{2} = 12 - 10 \sqrt{2}$$
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
$$a = 1$$
$$b = -24$$
$$c = -56$$
, then
D = b^2 - 4 * a * c =
(-24)^2 - 4 * (1) * (-56) = 800
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 12 + 10 \sqrt{2}$$
$$x_{2} = 12 - 10 \sqrt{2}$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -24$$
$$q = \frac{c}{a}$$
$$q = -56$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 24$$
$$x_{1} x_{2} = -56$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -24$$
$$q = \frac{c}{a}$$
$$q = -56$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 24$$
$$x_{1} x_{2} = -56$$
Sum and product of roots
[src]
sum
___ ___ 12 - 10*\/ 2 + 12 + 10*\/ 2
$$\left(12 - 10 \sqrt{2}\right) + \left(12 + 10 \sqrt{2}\right)$$
=
24
$$24$$
product
/ ___\ / ___\ \12 - 10*\/ 2 /*\12 + 10*\/ 2 /
$$\left(12 - 10 \sqrt{2}\right) \left(12 + 10 \sqrt{2}\right)$$
=
-56
$$-56$$
-56
Rapid solution
[src]
___ x1 = 12 - 10*\/ 2
$$x_{1} = 12 - 10 \sqrt{2}$$
___ x2 = 12 + 10*\/ 2
$$x_{2} = 12 + 10 \sqrt{2}$$
x2 = 12 + 10*sqrt(2)