Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2x=0
-
Equation -5*x=25
-
Equation 5*sin(x)+cos(x)=5
-
Equation 25*x^2=16
- Express {x} in terms of y where:
- -11*x-1*y=12
- 6*x+4*y=15
- 3*x+19*y=4
- 8*x-9*y=-1
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Identical expressions
- (x- six)(-5x- nine)= zero
- (x minus 6)( minus 5x minus 9) equally 0
- (x minus six)( minus 5x minus nine) equally zero
- x-6-5x-9=0
- (x-6)(-5x-9)=O
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Similar expressions
- (x+6)(-5x-9)=0
- (x-6)(5x-9)=0
- (x-6)(-5x+9)=0
(x-6)(-5x-9)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(- 5 x - 9\right) \left(x - 6\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} + 21 x + 54 = 0$$
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
$$a = -5$$
$$b = 21$$
$$c = 54$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{9}{5}$$
$$x_{2} = 6$$
$$\left(- 5 x - 9\right) \left(x - 6\right) = 0$$
We get the quadratic equation
$$- 5 x^{2} + 21 x + 54 = 0$$
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
$$a = -5$$
$$b = 21$$
$$c = 54$$
, then
D = b^2 - 4 * a * c =
(21)^2 - 4 * (-5) * (54) = 1521
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{9}{5}$$
$$x_{2} = 6$$
Sum and product of roots
[src]
sum
6 - 9/5
$$- \frac{9}{5} + 6$$
=
21/5
$$\frac{21}{5}$$
product
6*(-9) ------ 5
$$\frac{\left(-9\right) 6}{5}$$
=
-54/5
$$- \frac{54}{5}$$
-54/5