Mister Exam
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How to use it?
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Identical expressions
- x^ two -13x+ twenty-two = zero
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- x2-13x+22=0
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- x^2-13x+22=O
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Similar expressions
- x^2+13x+22=0
- x^2-13x-22=0
x^2-13x+22=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
$$a = 1$$
$$b = -13$$
$$c = 22$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 11$$
$$x_{2} = 2$$
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
$$a = 1$$
$$b = -13$$
$$c = 22$$
, then
D = b^2 - 4 * a * c =
(-13)^2 - 4 * (1) * (22) = 81
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 11$$
$$x_{2} = 2$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -13$$
$$q = \frac{c}{a}$$
$$q = 22$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 13$$
$$x_{1} x_{2} = 22$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -13$$
$$q = \frac{c}{a}$$
$$q = 22$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 13$$
$$x_{1} x_{2} = 22$$
Sum and product of roots
[src]
sum
2 + 11
$$2 + 11$$
=
13
$$13$$
product
2*11
$$2 \cdot 11$$
=
22
$$22$$
22
The graph