Mister Exam
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- 4x2−24x-20=0.
4x2−24x+20=0. equation
The teacher will be very surprised to see your correct solution 😉
The solution
The graph
Sum and product of roots
[src]
sum
5 re(x2) I*im(x2) - + ------ + -------- 6 6 6
$$\frac{\operatorname{re}{\left(x_{2}\right)}}{6} + \frac{i \operatorname{im}{\left(x_{2}\right)}}{6} + \frac{5}{6}$$
=
5 re(x2) I*im(x2) - + ------ + -------- 6 6 6
$$\frac{\operatorname{re}{\left(x_{2}\right)}}{6} + \frac{i \operatorname{im}{\left(x_{2}\right)}}{6} + \frac{5}{6}$$
product
5 re(x2) I*im(x2) - + ------ + -------- 6 6 6
$$\frac{\operatorname{re}{\left(x_{2}\right)}}{6} + \frac{i \operatorname{im}{\left(x_{2}\right)}}{6} + \frac{5}{6}$$
=
5 re(x2) I*im(x2) - + ------ + -------- 6 6 6
$$\frac{\operatorname{re}{\left(x_{2}\right)}}{6} + \frac{i \operatorname{im}{\left(x_{2}\right)}}{6} + \frac{5}{6}$$
5/6 + re(x2)/6 + i*im(x2)/6
Rapid solution
[src]
5 re(x2) I*im(x2)
x1 = - + ------ + --------
6 6 6
$$x_{1} = \frac{\operatorname{re}{\left(x_{2}\right)}}{6} + \frac{i \operatorname{im}{\left(x_{2}\right)}}{6} + \frac{5}{6}$$
x1 = re(x2)/6 + i*im(x2)/6 + 5/6