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Equation (x-5)(x-1)-21=0
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(x-5)(x-1)-21=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x - 5\right) \left(x - 1\right) - 21 = 0$$
We get the quadratic equation
$$x^{2} - 6 x - 16 = 0$$
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
$$a = 1$$
$$b = -6$$
$$c = -16$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 8$$
$$x_{2} = -2$$
$$\left(x - 5\right) \left(x - 1\right) - 21 = 0$$
We get the quadratic equation
$$x^{2} - 6 x - 16 = 0$$
This equation is of the form
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
$$a = 1$$
$$b = -6$$
$$c = -16$$
, then
D = b^2 - 4 * a * c =
(-6)^2 - 4 * (1) * (-16) = 100
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 8$$
$$x_{2} = -2$$
Sum and product of roots
[src]
sum
-2 + 8
$$-2 + 8$$
=
6
$$6$$
product
-2*8
$$- 16$$
=
-16
$$-16$$
-16
The graph