Solve the quadratic equation?

Question

2z^2+10z+15=0

Answer 1

Use the quadratic formula.

Answer 2

To solve this, we need to use the quadratic formula. Reminder that

z = [-10 +/- sqrt(10^2 - 4(2)(15))]/2(2)
z = [-10 +/- sqrt (-20)]/4
z = [-10 +/- 2 sqrt(-5)]/4

Notice that we have all constants that are a multiple of 2, so we divide each one by 2.
z = [-5 +/- sqrt(-5)]/2
z = [-5 +/- i sqrt(5)]/2
z = -5/2 +/- sqrt(5)i

Notice we can't take the square root of a negative number, so in the realm of real numbers, there are no real solutions. The ones I've given are complex solutions, where i = sqrt(-1).

Answer 3

2z² + 10z + 15

a = 2

b = 10

c = 15

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Quadratic formula

x = - b ± √b² - 4ac/2a

x = - 10 ± √(10)² - 4(2)(15)/2(2)

x = - 10 ± √100 - 4(30) / 4

x = -10 ± √100 - 120 / 4

x = - 10 ± √- 20 / 4

x = - 10 ± √- 5 √4 / 4

x = - 10 ± 2 √- 5 / 4

x = - 5 ± 2 √- 5 / 2

x = - 5/2 ± √- 5

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