How do you solve $3z^2+10z+15=0$ ?

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Answer 1 · 2015-06-15T23:07:54

The discriminant is negative, so I would use the quadratic formula directly to get:

$z = (-5 +- 2sqrt(5) i)/3$

$3z^2+10z+15$ is of the form $az^2+bz+c$ with $a=3$ , $b=10$ and $c=15$ .

This has discriminant $Delta$ given by the formula:

$Delta = b^2-4ac = 10^2 - (4xx3xx15) = 100 - 180 = -80$

Since this is negative the quadratic equation has two distinct complex roots.

The roots are given by the quadratic formula:

$z = (-b+-sqrt(Delta))/(2a) = (-10+-sqrt(-80))/(2*3)$

$=(-10+-sqrt(80)i)/6$

$=(-10+-sqrt(16*5)i)/6$

$=(-10+-4sqrt(5)i)/6$

$=(-5+-2sqrt(5)i)/3$

How do you solve 3z^2+10z+15=03z^2+10z+15=0?