Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 6-5(4x-1)=3
-
Equation (x-2)(-2x-3)=0
-
Equation x+5=7
-
Equation |3|x|-5|=-2x-2
- Express {x} in terms of y where:
- 4*x+13*y=8
- 3*x-11*y=20
- 8*x-4*y=10
- -6*x-11*y=-20
-
Identical expressions
- (x- two)(-2x- three)= zero
- (x minus 2)( minus 2x minus 3) equally 0
- (x minus two)( minus 2x minus three) equally zero
- x-2-2x-3=0
- (x-2)(-2x-3)=O
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Similar expressions
- (x-2)(2x-3)=0
- 3*(x-2)-2*(x-3)=0
- (x-2)*(-2x-3)=0
- (x-2)(-2x+3)=0
- (x+2)(-2x-3)=0
(x-2)(-2x-3)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(- 2 x - 3\right) \left(x - 2\right) = 0$$
We get the quadratic equation
$$- 2 x^{2} + x + 6 = 0$$
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
$$a = -2$$
$$b = 1$$
$$c = 6$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{3}{2}$$
$$x_{2} = 2$$
$$\left(- 2 x - 3\right) \left(x - 2\right) = 0$$
We get the quadratic equation
$$- 2 x^{2} + x + 6 = 0$$
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
$$a = -2$$
$$b = 1$$
$$c = 6$$
, then
D = b^2 - 4 * a * c =
(1)^2 - 4 * (-2) * (6) = 49
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{3}{2}$$
$$x_{2} = 2$$
Sum and product of roots
[src]
sum
2 - 3/2
$$- \frac{3}{2} + 2$$
=
1/2
$$\frac{1}{2}$$
product
2*(-3) ------ 2
$$\frac{\left(-3\right) 2}{2}$$
=
-3
$$-3$$
-3
The graph