Mister Exam
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Identical expressions
- (5x+ two)*(-x- four)= zero
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Similar expressions
- 0(5x+2)(-x-4)=0
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(5x+2)*(-x-4)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(- x - 4\right) \left(5 x + 2\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} - 22 x - 8 = 0$$
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
$$a = -5$$
$$b = -22$$
$$c = -8$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -4$$
$$x_{2} = - \frac{2}{5}$$
$$\left(- x - 4\right) \left(5 x + 2\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} - 22 x - 8 = 0$$
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
$$a = -5$$
$$b = -22$$
$$c = -8$$
, then
D = b^2 - 4 * a * c =
(-22)^2 - 4 * (-5) * (-8) = 324
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -4$$
$$x_{2} = - \frac{2}{5}$$
Sum and product of roots
[src]
sum
-4 - 2/5
$$-4 - \frac{2}{5}$$
=
-22/5
$$- \frac{22}{5}$$
product
-4*(-2) ------- 5
$$- \frac{-8}{5}$$
=
8/5
$$\frac{8}{5}$$
8/5
The graph