Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x+2)/9=(x-3)/2
-
Equation 11+2x=55+3x
-
Equation (x-2)^4+3*(x-2)^2-10=0
-
Equation 3*x^2-18=0
- Express {x} in terms of y where:
- 2*x+3*y=14
- 18*x-8*y=-2
- 16*x-7*y=-5
- 10*x-16*y=-6
- Graphing y =:
- 3-3*x^2
- Derivative of:
-
3-3*x^2
- Factor polynomial:
- 3-3*x^2
-
Identical expressions
- three - three *x^ two = zero
- 3 minus 3 multiply by x squared equally 0
- three minus three multiply by x to the power of two equally zero
- 3-3*x2=0
- 3-3*x²=0
- 3-3*x to the power of 2=0
- 3-3x^2=0
- 3-3x2=0
- 3-3*x^2=O
-
Similar expressions
- 3+3*x^2=0
- -2*x^3-3*x^2+18=0
3-3*x^2=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
$$a = -3$$
$$b = 0$$
$$c = 3$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = -1$$
Simplify
$$x_{2} = 1$$
Simplify
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
$$a = -3$$
$$b = 0$$
$$c = 3$$
, then
D = b^2 - 4 * a * c =
(0)^2 - 4 * (-3) * (3) = 36
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = -1$$
Simplify
$$x_{2} = 1$$
Simplify
Vieta's Theorem
rewrite the equation
$$- 3 x^{2} + 3 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 1 = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -1$$
$$- 3 x^{2} + 3 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} - 1 = 0$$
$$p x + x^{2} + q = 0$$
where
$$p = \frac{b}{a}$$
$$p = 0$$
$$q = \frac{c}{a}$$
$$q = -1$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 0$$
$$x_{1} x_{2} = -1$$
Sum and product of roots
[src]
sum
0 - 1 + 1
$$\left(-1 + 0\right) + 1$$
=
0
$$0$$
product
1*-1*1
$$1 \left(-1\right) 1$$
=
-1
$$-1$$
-1
The graph