Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 8x-15=-12+5x
-
Equation x^2-x-7=0
-
Equation 141*10^(-6)*x*3*sqrt(2)=sqrt((1-19881*10^(-12)*x^2)^2+9)
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Equation x^3-6*x^2+x-6=0
- Express {x} in terms of y where:
- -19*x+1*y=-6
- 16*x-9*y=-17
- 2*x+4*y=-1
- -14*x-5*y=-3
-
Identical expressions
- (x- two)(x+ nineteen)= zero
- (x minus 2)(x plus 19) equally 0
- (x minus two)(x plus nineteen) equally zero
- x-2x+19=0
- (x-2)(x+19)=O
-
Similar expressions
- (x+2)(x+19)=0
- (x-2)(x-19)=0
(x-2)(x+19)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x - 2\right) \left(x + 19\right) = 0$$
We get the quadratic equation
$$x^{2} + 17 x - 38 = 0$$
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
$$a = 1$$
$$b = 17$$
$$c = -38$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 2$$
$$x_{2} = -19$$
$$\left(x - 2\right) \left(x + 19\right) = 0$$
We get the quadratic equation
$$x^{2} + 17 x - 38 = 0$$
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
$$a = 1$$
$$b = 17$$
$$c = -38$$
, then
D = b^2 - 4 * a * c =
(17)^2 - 4 * (1) * (-38) = 441
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 2$$
$$x_{2} = -19$$
Sum and product of roots
[src]
sum
-19 + 2
$$-19 + 2$$
=
-17
$$-17$$
product
-19*2
$$- 38$$
=
-38
$$-38$$
-38