How do you solve the quadratic using the quadratic formula given $3 d^{2} - 5 d + 6 = 0$ $3d^2-5d+6=0$ over the set of complex numbers?

Question

How do you solve the quadratic using the quadratic formula given $3 d^{2} - 5 d + 6 = 0$ $3d^2-5d+6=0$ over the set of complex numbers?

1 Answer

Impact of this question

1533 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-11T10:38:15

$d = \frac{5}{6} + \frac{\sqrt{47}}{6} i XX or XX d = \frac{5}{6} - \frac{\sqrt{47}}{6} i$ $d=5/6+sqrt(47)/6icolor(white)("XX")orcolor(white)("XX")d=5/6-sqrt(47)/6i$

Explanation:

For a parabolic equation of the form:
$XXX a d^{2} + b d + c = 0$ $color(white)("XXX")color(red)ad^2+color(blue)bd+color(green)c=0$
the quadratic formula gives the solution as
$XXX d = \frac{- b \pm \sqrt{b^{2} + 4 a c}}{2 a}$ $color(white)("XXX")d=(-color(blue)b+-sqrt(color(blue)b^2+4color(red)acolor(green)c))/(2color(red)a)$
$XXXXXXXXXX$ $color(white)("XXXXXXXXXX")$ over the set of complex numbers

For the given example:
$XXX a = 3$ $color(white)("XXX")color(red)a=color(red)3$
$XXX b = - 5$ $color(white)("XXX")color(blue)b=color(blue)(-5)$
$XXX c = 6$ $color(white)("XXX")color(green)c=color(green)6$

Therefore
$XXX d = \frac{- (- 5) \pm \sqrt{{(- 5)}^{2} - 4 \times 3 \times 6}}{2 \times 3}$ $color(white)("XXX")d=(-color(blue)(""(-5))+-sqrt(color(blue)(""(-5))^2-4xxcolor(red)3xxcolor(green)6))/(2xxcolor(red)3)$

$XXX = \frac{5 \pm \sqrt{- 47}}{6}$ $color(white)("XXX")=(5+-sqrt(-47))/6$

$d = \frac{5}{6} + \frac{\sqrt{47}}{6} i XX or XX d = \frac{5}{6} - \frac{\sqrt{47}}{6} i$ $d=5/6+sqrt(47)/6icolor(white)("XX")orcolor(white)("XX")d=5/6-sqrt(47)/6i$

Science

Math

Humanities

... and beyond

How do you solve the quadratic using the quadratic formula given $3 d^{2} - 5 d + 6 = 0$ $3d^2-5d+6=0$ over the set of complex numbers?

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you solve the quadratic using the quadratic formula given 3d2−5d+6=03d^2-5d+6=0 over the set of complex numbers?

1 Answer

Explanation:

Related questions

Impact of this question

How do you solve the quadratic using the quadratic formula given $3 d^{2} - 5 d + 6 = 0$ $3d^2-5d+6=0$ over the set of complex numbers?