Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation -5*x=25
-
Equation 25*x^2=16
- Equation 3*x^2-48=0
-
Equation x^3+4*x^2-9*x-36=0
- Express {x} in terms of y where:
- 13*x-1*y=-20
- -2*x-18*y=10
- -12*x-11*y=19
- -6*x+11*y=-5
- Derivative of:
-
3x^2+2
-
-5x
- Graphing y =:
- 3x^2+2
- -5x
- Integral of d{x}:
- 3x^2+2
-
-5x
-
Identical expressions
- 3x^ two + two =-5x
- 3x squared plus 2 equally minus 5x
- 3x to the power of two plus two equally minus 5x
- 3x2+2=-5x
- 3x²+2=-5x
- 3x to the power of 2+2=-5x
-
Similar expressions
- -5*x=25
- 3x^2+2=+5x
- (-5*x-3)*(2*x-5)=0
- 3x^2-2=-5x
- x^2-5*x+7=0
3x^2+2=-5x equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Move right part of the equation to
left part with negative sign.
The equation is transformed from
$$3 x^{2} + 2 = - 5 x$$
to
$$5 x + \left(3 x^{2} + 2\right) = 0$$
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
$$a = 3$$
$$b = 5$$
$$c = 2$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = - \frac{2}{3}$$
$$x_{2} = -1$$
left part with negative sign.
The equation is transformed from
$$3 x^{2} + 2 = - 5 x$$
to
$$5 x + \left(3 x^{2} + 2\right) = 0$$
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
$$a = 3$$
$$b = 5$$
$$c = 2$$
, then
D = b^2 - 4 * a * c =
(5)^2 - 4 * (3) * (2) = 1
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{2}{3}$$
$$x_{2} = -1$$
Vieta's Theorem
rewrite the equation
$$3 x^{2} + 2 = - 5 x$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{5 x}{3} + \frac{2}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{5}{3}$$
$$q = \frac{c}{a}$$
$$q = \frac{2}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{5}{3}$$
$$x_{1} x_{2} = \frac{2}{3}$$
$$3 x^{2} + 2 = - 5 x$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{5 x}{3} + \frac{2}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{5}{3}$$
$$q = \frac{c}{a}$$
$$q = \frac{2}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{5}{3}$$
$$x_{1} x_{2} = \frac{2}{3}$$
Sum and product of roots
[src]
sum
-1 - 2/3
$$-1 - \frac{2}{3}$$
=
-5/3
$$- \frac{5}{3}$$
product
-(-2) ------ 3
$$- \frac{-2}{3}$$
=
2/3
$$\frac{2}{3}$$
2/3
The graph