Mister Exam
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- x^ two -17x+ seventy-two = zero
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Similar expressions
- x^2-17x-72=0
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x^2-17x+72=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
$$a = 1$$
$$b = -17$$
$$c = 72$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 9$$
$$x_{2} = 8$$
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
$$a = 1$$
$$b = -17$$
$$c = 72$$
, then
D = b^2 - 4 * a * c =
(-17)^2 - 4 * (1) * (72) = 1
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 9$$
$$x_{2} = 8$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -17$$
$$q = \frac{c}{a}$$
$$q = 72$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 17$$
$$x_{1} x_{2} = 72$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -17$$
$$q = \frac{c}{a}$$
$$q = 72$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 17$$
$$x_{1} x_{2} = 72$$
Sum and product of roots
[src]
sum
8 + 9
$$8 + 9$$
=
17
$$17$$
product
8*9
$$8 \cdot 9$$
=
72
$$72$$
72
The graph