Mister Exam
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How to use it?
- Equation:
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Equation x^2-9*x=0
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Equation (5x-4)(6-x)=0
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Identical expressions
- (5x- four)(six -x)= zero
- (5x minus 4)(6 minus x) equally 0
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Similar expressions
- (5x-4)(6+x)=0
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(5x-4)(6-x)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(6 - x\right) \left(5 x - 4\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} + 34 x - 24 = 0$$
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
$$a = -5$$
$$b = 34$$
$$c = -24$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{4}{5}$$
$$x_{2} = 6$$
$$\left(6 - x\right) \left(5 x - 4\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} + 34 x - 24 = 0$$
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
$$a = -5$$
$$b = 34$$
$$c = -24$$
, then
D = b^2 - 4 * a * c =
(34)^2 - 4 * (-5) * (-24) = 676
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{4}{5}$$
$$x_{2} = 6$$
Sum and product of roots
[src]
sum
6 + 4/5
$$\frac{4}{5} + 6$$
=
34/5
$$\frac{34}{5}$$
product
6*4 --- 5
$$\frac{4 \cdot 6}{5}$$
=
24/5
$$\frac{24}{5}$$
24/5
The graph