Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2-3x+1=0
-
Equation x^2-5*x-5=0
-
Equation x^2+4*x-5=0
- Equation x+y=4
- Express {x} in terms of y where:
- 1*x+6*y=-6
- -5*x-2*y=9
- 1*x+11*y=-3
- 17*x-19*y=-12
-
Identical expressions
- (x- thirteen)*(x+ eight)= zero
- (x minus 13) multiply by (x plus 8) equally 0
- (x minus thirteen) multiply by (x plus eight) equally zero
- (x-13)(x+8)=0
- x-13x+8=0
- (x-13)*(x+8)=O
-
Similar expressions
- (x-13)*(x-8)=0
- (x+13)*(x+8)=0
(x-13)*(x+8)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x - 13\right) \left(x + 8\right) = 0$$
We get the quadratic equation
$$x^{2} - 5 x - 104 = 0$$
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
$$a = 1$$
$$b = -5$$
$$c = -104$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 13$$
$$x_{2} = -8$$
$$\left(x - 13\right) \left(x + 8\right) = 0$$
We get the quadratic equation
$$x^{2} - 5 x - 104 = 0$$
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
$$a = 1$$
$$b = -5$$
$$c = -104$$
, then
D = b^2 - 4 * a * c =
(-5)^2 - 4 * (1) * (-104) = 441
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 13$$
$$x_{2} = -8$$
Sum and product of roots
[src]
sum
-8 + 13
$$-8 + 13$$
=
5
$$5$$
product
-8*13
$$- 104$$
=
-104
$$-104$$
-104