Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x+12=5
-
Equation 3/(x-5)+8/x=2
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Equation (5x-2)*(-x+3)=0
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Equation 1-x/2=x/3
- Express {x} in terms of y where:
- 18*x+17*y=-14
- 16*x-17*y=-15
- -4*x-4*y=19
- 12*x+1*y=15
-
Identical expressions
- (5x- two)*(-x+ three)= zero
- (5x minus 2) multiply by ( minus x plus 3) equally 0
- (5x minus two) multiply by ( minus x plus three) equally zero
- (5x-2)(-x+3)=0
- 5x-2-x+3=0
- (5x-2)*(-x+3)=O
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Similar expressions
- (5x-2)(-x+3)=0
- (5x-2)*(-x-3)=0
- (5x+2)*(-x+3)=0
- (5x-2)*(x+3)=0
(5x-2)*(-x+3)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(3 - x\right) \left(5 x - 2\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} + 17 x - 6 = 0$$
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
$$a = -5$$
$$b = 17$$
$$c = -6$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = \frac{2}{5}$$
$$x_{2} = 3$$
$$\left(3 - x\right) \left(5 x - 2\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} + 17 x - 6 = 0$$
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
$$a = -5$$
$$b = 17$$
$$c = -6$$
, then
D = b^2 - 4 * a * c =
(17)^2 - 4 * (-5) * (-6) = 169
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = \frac{2}{5}$$
$$x_{2} = 3$$
Sum and product of roots
[src]
sum
3 + 2/5
$$\frac{2}{5} + 3$$
=
17/5
$$\frac{17}{5}$$
product
3*2 --- 5
$$\frac{2 \cdot 3}{5}$$
=
6/5
$$\frac{6}{5}$$
6/5
The graph