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- Equation:
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Equation x^2-8*x+17=0
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Identical expressions
- x^ two - eight *x+ seventeen = zero
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Similar expressions
- x^2+8*x+17=0
- x^2-8*x-17=0
x^2-8*x+17=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
$$a = 1$$
$$b = -8$$
$$c = 17$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = 4 + i$$
$$x_{2} = 4 - i$$
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
$$a = 1$$
$$b = -8$$
$$c = 17$$
, then
D = b^2 - 4 * a * c =
(-8)^2 - 4 * (1) * (17) = -4
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4 + i$$
$$x_{2} = 4 - i$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = 17$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = 17$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -8$$
$$q = \frac{c}{a}$$
$$q = 17$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 8$$
$$x_{1} x_{2} = 17$$
Sum and product of roots
[src]
sum
4 - I + 4 + I
$$\left(4 - i\right) + \left(4 + i\right)$$
=
8
$$8$$
product
(4 - I)*(4 + I)
$$\left(4 - i\right) \left(4 + i\right)$$
=
17
$$17$$
17
The graph