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
- -9*x-6*y=12
-
Identical expressions
- (- five *x- three)*(two *x- five)= zero
- ( minus 5 multiply by x minus 3) multiply by (2 multiply by x minus 5) equally 0
- ( minus five multiply by x minus three) multiply by (two multiply by x minus five) equally zero
- (-5x-3)(2x-5)=0
- -5x-32x-5=0
- (-5*x-3)*(2*x-5)=O
-
Similar expressions
- (-5*x+3)*(2*x-5)=0
- (-5x-3)(2x-5)2*x^2+6*x+9=0
- (-5*x-3)*(2*x+5)=0
- (5*x-3)*(2*x-5)=0
(-5*x-3)*(2*x-5)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(- 5 x - 3\right) \left(2 x - 5\right) = 0$$
We get the quadratic equation
$$- 10 x^{2} + 19 x + 15 = 0$$
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
$$a = -10$$
$$b = 19$$
$$c = 15$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{3}{5}$$
$$x_{2} = \frac{5}{2}$$
$$\left(- 5 x - 3\right) \left(2 x - 5\right) = 0$$
We get the quadratic equation
$$- 10 x^{2} + 19 x + 15 = 0$$
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
$$a = -10$$
$$b = 19$$
$$c = 15$$
, then
D = b^2 - 4 * a * c =
(19)^2 - 4 * (-10) * (15) = 961
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{3}{5}$$
$$x_{2} = \frac{5}{2}$$
Sum and product of roots
[src]
sum
-3/5 + 5/2
$$- \frac{3}{5} + \frac{5}{2}$$
=
19 -- 10
$$\frac{19}{10}$$
product
-3*5 ---- 5*2
$$- \frac{3}{2}$$
=
-3/2
$$- \frac{3}{2}$$
-3/2
The graph