Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x-4)/(x-6)=2
-
Equation e^x=2
-
Equation x^2=-12
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Equation x^2+4*x=21
- Express {x} in terms of y where:
- 19*x-3*y=-12
- 17*x-7*y=15
- -15*x-3*y=7
- 15*x+10*y=13
-
Identical expressions
- (x- four)*(x+ seven)= zero
- (x minus 4) multiply by (x plus 7) equally 0
- (x minus four) multiply by (x plus seven) equally zero
- (x-4)(x+7)=0
- x-4x+7=0
- (x-4)*(x+7)=O
-
Similar expressions
- (x-4)*(x-7)=0
- (x+4)*(x+7)=0
(x-4)*(x+7)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x - 4\right) \left(x + 7\right) = 0$$
We get the quadratic equation
$$x^{2} + 3 x - 28 = 0$$
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
$$a = 1$$
$$b = 3$$
$$c = -28$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 4$$
$$x_{2} = -7$$
$$\left(x - 4\right) \left(x + 7\right) = 0$$
We get the quadratic equation
$$x^{2} + 3 x - 28 = 0$$
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
$$a = 1$$
$$b = 3$$
$$c = -28$$
, then
D = b^2 - 4 * a * c =
(3)^2 - 4 * (1) * (-28) = 121
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 4$$
$$x_{2} = -7$$
Sum and product of roots
[src]
sum
-7 + 4
$$-7 + 4$$
=
-3
$$-3$$
product
-7*4
$$- 28$$
=
-28
$$-28$$
-28
The graph