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Identical expressions
- 4x2-11x- three / three -x= zero
- 4x2 minus 11x minus 3 divide by 3 minus x equally 0
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Similar expressions
- 4x2+11x-3/3-x=0
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4x2-11x-3/3-x=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
4*x2 - 11*x - 1 - x = 0
$$- x + \left(\left(- 11 x + 4 x_{2}\right) - 1\right) = 0$$
The graph
Rapid solution
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1 re(x2) I*im(x2)
x1 = - -- + ------ + --------
12 3 3
$$x_{1} = \frac{\operatorname{re}{\left(x_{2}\right)}}{3} + \frac{i \operatorname{im}{\left(x_{2}\right)}}{3} - \frac{1}{12}$$
x1 = re(x2)/3 + i*im(x2)/3 - 1/12
Sum and product of roots
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sum
1 re(x2) I*im(x2) - -- + ------ + -------- 12 3 3
$$\frac{\operatorname{re}{\left(x_{2}\right)}}{3} + \frac{i \operatorname{im}{\left(x_{2}\right)}}{3} - \frac{1}{12}$$
=
1 re(x2) I*im(x2) - -- + ------ + -------- 12 3 3
$$\frac{\operatorname{re}{\left(x_{2}\right)}}{3} + \frac{i \operatorname{im}{\left(x_{2}\right)}}{3} - \frac{1}{12}$$
product
1 re(x2) I*im(x2) - -- + ------ + -------- 12 3 3
$$\frac{\operatorname{re}{\left(x_{2}\right)}}{3} + \frac{i \operatorname{im}{\left(x_{2}\right)}}{3} - \frac{1}{12}$$
=
1 re(x2) I*im(x2) - -- + ------ + -------- 12 3 3
$$\frac{\operatorname{re}{\left(x_{2}\right)}}{3} + \frac{i \operatorname{im}{\left(x_{2}\right)}}{3} - \frac{1}{12}$$
-1/12 + re(x2)/3 + i*im(x2)/3