Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 4=7-6(5x-1)
-
Equation 5=12-5(4x-1)
-
Equation x*40+3800=6400
-
Equation 3*x-6=x+4
- Express {x} in terms of y where:
- 8*x-12*y=9
- 17*x-15*y=17
- -9*x-6*y=12
- -6*x+11*y=-5
-
Identical expressions
- one , five *x^ two + twenty *x+ seventy-one = zero
- 1,5 multiply by x squared plus 20 multiply by x plus 71 equally 0
- one , five multiply by x to the power of two plus twenty multiply by x plus seventy minus one equally zero
- 1,5*x2+20*x+71=0
- 1,5*x²+20*x+71=0
- 1,5*x to the power of 2+20*x+71=0
- 1,5x^2+20x+71=0
- 1,5x2+20x+71=0
- 1,5*x^2+20*x+71=O
-
Similar expressions
- 1,5*x^2-20*x+71=0
- 1,5*x^2+20*x-71=0
1,5*x^2+20*x+71=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2 3*x ---- + 20*x + 71 = 0 2
$$\left(\frac{3 x^{2}}{2} + 20 x\right) + 71 = 0$$
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
$$a = \frac{3}{2}$$
$$b = 20$$
$$c = 71$$
, then
Because D<0, then the equation
has no real roots,
but complex roots is exists.
or
$$x_{1} = - \frac{20}{3} + \frac{\sqrt{26} i}{3}$$
$$x_{2} = - \frac{20}{3} - \frac{\sqrt{26} i}{3}$$
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
$$a = \frac{3}{2}$$
$$b = 20$$
$$c = 71$$
, then
D = b^2 - 4 * a * c =
(20)^2 - 4 * (3/2) * (71) = -26
Because D<0, then the equation
has no real roots,
but complex roots is exists.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = - \frac{20}{3} + \frac{\sqrt{26} i}{3}$$
$$x_{2} = - \frac{20}{3} - \frac{\sqrt{26} i}{3}$$
Vieta's Theorem
rewrite the equation
$$\left(\frac{3 x^{2}}{2} + 20 x\right) + 71 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{40 x}{3} + \frac{142}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{40}{3}$$
$$q = \frac{c}{a}$$
$$q = \frac{142}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{40}{3}$$
$$x_{1} x_{2} = \frac{142}{3}$$
$$\left(\frac{3 x^{2}}{2} + 20 x\right) + 71 = 0$$
of
$$a x^{2} + b x + c = 0$$
as reduced quadratic equation
$$x^{2} + \frac{b x}{a} + \frac{c}{a} = 0$$
$$x^{2} + \frac{40 x}{3} + \frac{142}{3} = 0$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = \frac{40}{3}$$
$$q = \frac{c}{a}$$
$$q = \frac{142}{3}$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = - \frac{40}{3}$$
$$x_{1} x_{2} = \frac{142}{3}$$
Rapid solution
[src]
____
20 I*\/ 26
x1 = - -- - --------
3 3
$$x_{1} = - \frac{20}{3} - \frac{\sqrt{26} i}{3}$$
____
20 I*\/ 26
x2 = - -- + --------
3 3
$$x_{2} = - \frac{20}{3} + \frac{\sqrt{26} i}{3}$$
x2 = -20/3 + sqrt(26)*i/3
Sum and product of roots
[src]
sum
____ ____ 20 I*\/ 26 20 I*\/ 26 - -- - -------- + - -- + -------- 3 3 3 3
$$\left(- \frac{20}{3} - \frac{\sqrt{26} i}{3}\right) + \left(- \frac{20}{3} + \frac{\sqrt{26} i}{3}\right)$$
=
-40/3
$$- \frac{40}{3}$$
product
/ ____\ / ____\ | 20 I*\/ 26 | | 20 I*\/ 26 | |- -- - --------|*|- -- + --------| \ 3 3 / \ 3 3 /
$$\left(- \frac{20}{3} - \frac{\sqrt{26} i}{3}\right) \left(- \frac{20}{3} + \frac{\sqrt{26} i}{3}\right)$$
=
142/3
$$\frac{142}{3}$$
142/3
Numerical answer
[src]
x1 = -6.66666666666667 - 1.69967317119759*i
x2 = -6.66666666666667 + 1.69967317119759*i
x2 = -6.66666666666667 + 1.69967317119759*i