Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^3=3
-
Equation 5-x^2=0
- Equation (-5*x+3)*(-x+8)=0
-
Equation x^2+6=5x
- Express {x} in terms of y where:
- -6*x+11*y=-5
- -3*x-19*y=-9
- -19*x-15*y=15
- 13*x-11*y=16
-
Identical expressions
- (- five *x+ three)*(-x+ eight)= zero
- ( minus 5 multiply by x plus 3) multiply by ( minus x plus 8) equally 0
- ( minus five multiply by x plus three) multiply by ( minus x plus eight) equally zero
- (-5x+3)(-x+8)=0
- -5x+3-x+8=0
- (-5*x+3)*(-x+8)=O
-
Similar expressions
- (-5*x-3)*(-x+8)=0
- (5*x+3)*(-x+8)=0
- (-5*x+3)*(-x-8)=0
- (-5*x+3)*(x+8)=0
- (-5x+3)(-x+8)=0
(-5*x+3)*(-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
$$\left(3 - 5 x\right) \left(8 - x\right) = 0$$
We get the quadratic equation
$$5 x^{2} - 43 x + 24 = 0$$
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
$$a = 5$$
$$b = -43$$
$$c = 24$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 8$$
$$x_{2} = \frac{3}{5}$$
$$\left(3 - 5 x\right) \left(8 - x\right) = 0$$
We get the quadratic equation
$$5 x^{2} - 43 x + 24 = 0$$
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
$$a = 5$$
$$b = -43$$
$$c = 24$$
, then
D = b^2 - 4 * a * c =
(-43)^2 - 4 * (5) * (24) = 1369
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 8$$
$$x_{2} = \frac{3}{5}$$
Sum and product of roots
[src]
sum
8 + 3/5
$$\frac{3}{5} + 8$$
=
43/5
$$\frac{43}{5}$$
product
8*3 --- 5
$$\frac{3 \cdot 8}{5}$$
=
24/5
$$\frac{24}{5}$$
24/5