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- Equation:
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Similar expressions
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(5x-8)(4x-3)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(4 x - 3\right) \left(5 x - 8\right) = 0$$
We get the quadratic equation
$$20 x^{2} - 47 x + 24 = 0$$
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
$$a = 20$$
$$b = -47$$
$$c = 24$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{8}{5}$$
$$x_{2} = \frac{3}{4}$$
$$\left(4 x - 3\right) \left(5 x - 8\right) = 0$$
We get the quadratic equation
$$20 x^{2} - 47 x + 24 = 0$$
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
$$a = 20$$
$$b = -47$$
$$c = 24$$
, then
D = b^2 - 4 * a * c =
(-47)^2 - 4 * (20) * (24) = 289
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{8}{5}$$
$$x_{2} = \frac{3}{4}$$
Sum and product of roots
[src]
sum
3/4 + 8/5
$$\frac{3}{4} + \frac{8}{5}$$
=
47 -- 20
$$\frac{47}{20}$$
product
3*8 --- 4*5
$$\frac{3 \cdot 8}{4 \cdot 5}$$
=
6/5
$$\frac{6}{5}$$
6/5
The graph