Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 3*x^2-x-5=0
-
Equation 3x+3=-2-7x
-
Equation 2x^2+6x=0
-
Equation 5x-3=2x
- Express {x} in terms of y where:
- -1*x+4*y=5
- -14*x-10*y=-1
- 12*x-1*y=-19
- -8*x-16*y=-20
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Identical expressions
- (x- three)*(x+ eleven)= zero
- (x minus 3) multiply by (x plus 11) equally 0
- (x minus three) multiply by (x plus eleven) equally zero
- (x-3)(x+11)=0
- x-3x+11=0
- (x-3)*(x+11)=O
-
Similar expressions
- (x+3)*(x+11)=0
- (x-3)*(x-11)=0
(x-3)*(x+11)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Expand the expression in the equation
$$\left(x - 3\right) \left(x + 11\right) = 0$$
We get the quadratic equation
$$x^{2} + 8 x - 33 = 0$$
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
$$a = 1$$
$$b = 8$$
$$c = -33$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 3$$
$$x_{2} = -11$$
$$\left(x - 3\right) \left(x + 11\right) = 0$$
We get the quadratic equation
$$x^{2} + 8 x - 33 = 0$$
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
$$a = 1$$
$$b = 8$$
$$c = -33$$
, then
D = b^2 - 4 * a * c =
(8)^2 - 4 * (1) * (-33) = 196
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 3$$
$$x_{2} = -11$$
Sum and product of roots
[src]
sum
-11 + 3
$$-11 + 3$$
=
-8
$$-8$$
product
-11*3
$$- 33$$
=
-33
$$-33$$
-33