Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2^x=6-x
-
Equation x^3=4
-
Equation x^2+2x+2=0
-
Equation 3/(x-5)+8/x=2
- Express {x} in terms of y where:
- -1*x-6*y=18
- 6*x-19*y=-18
- -14*x+18*y=0
- -8*x+3*y=-4
- Integral of d{x}:
- 3*x^2+12*x
- Factor polynomial:
- 3*x^2+12*x
-
Identical expressions
- three *x^ two + twelve *x= zero
- 3 multiply by x squared plus 12 multiply by x equally 0
- three multiply by x to the power of two plus twelve multiply by x equally zero
- 3*x2+12*x=0
- 3*x²+12*x=0
- 3*x to the power of 2+12*x=0
- 3x^2+12x=0
- 3x2+12x=0
- 3*x^2+12*x=O
-
Similar expressions
- 3*x^2-12*x=0
3*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
$$a = 3$$
$$b = 12$$
$$c = 0$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 0$$
$$x_{2} = -4$$
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
$$a = 3$$
$$b = 12$$
$$c = 0$$
, then
D = b^2 - 4 * a * c =
(12)^2 - 4 * (3) * (0) = 144
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 0$$
$$x_{2} = -4$$
Vieta's Theorem
rewrite the equation
$$3 x^{2} + 12 x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + 4 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = 0$$
$$3 x^{2} + 12 x = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + 4 x = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = 4$$
$$q = \frac{c}{a}$$
$$q = 0$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = -4$$
$$x_{1} x_{2} = 0$$
The graph