Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x+(x*3)=168
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Equation t-4/25=8
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Equation x^2+12*x=0
-
Equation x^3=4x
- Express {x} in terms of y where:
- 15*x+2*y=8
- 1*x+4*y=-11
- 5*x-18*y=-17
- 17*x-5*y=15
- Factor polynomial:
- x^2+12*x
-
Identical expressions
- x^ two + twelve *x= zero
- x squared plus 12 multiply by x equally 0
- x to the power of two plus twelve multiply by x equally zero
- x2+12*x=0
- x²+12*x=0
- x to the power of 2+12*x=0
- x^2+12x=0
- x2+12x=0
- x^2+12*x=O
-
Similar expressions
- x^2-12*x=0
x^2+12*x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
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
$$a = 1$$
$$b = 12$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = -12$$
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
$$a = 1$$
$$b = 12$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(12)^2 - 4 * (1) * (0) = 144
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = -12$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 12$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -12$$
$$x_{1} x_{2} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 12$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -12$$
$$x_{1} x_{2} = 0$$
The graph