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Similar expressions
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(-5*x-3)*(2*x-1)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(- 5 x - 3\right) \left(2 x - 1\right) = 0$$
We get the quadratic equation
$$- 10 x^{2} - x + 3 = 0$$
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
$$a = -10$$
$$b = -1$$
$$c = 3$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{3}{5}$$
$$x_{2} = \frac{1}{2}$$
$$\left(- 5 x - 3\right) \left(2 x - 1\right) = 0$$
We get the quadratic equation
$$- 10 x^{2} - x + 3 = 0$$
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
$$a = -10$$
$$b = -1$$
$$c = 3$$
, then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (-10) * (3) = 121
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{3}{5}$$
$$x_{2} = \frac{1}{2}$$
Sum and product of roots
[src]
sum
-3/5 + 1/2
$$- \frac{3}{5} + \frac{1}{2}$$
=
-1/10
$$- \frac{1}{10}$$
product
-3 --- 5*2
$$- \frac{3}{10}$$
=
-3/10
$$- \frac{3}{10}$$
-3/10
The graph