How do you solve 3z ^ { 2} + 4z - 7= 0?

2 Answers

z=-7/3 or z = 1

Explanation:

Using the quadratic equation

z_(1,2) = (-b +- sqrt(b^2 –4ac))/(2a)

you get

z= (-4 +- sqrt( 4^2 -4xx3xx (-7)))/(2xx3)

z= (-4 +- sqrt(16+84))/6

z= (-4 +- sqrt(100))/6

z= (-4 +- 10)/6

z= -14/6 or z = 6/6

z=-14/6 or z = 1

z= -7/3 or z = 1

Apr 4, 2018

1, and -7/3

Explanation:

3z^2 + 4z - 7 = 0
Use shortcut when a + b + c = 0
z = 1, and z = c/a = - 7/3

Reminder of shortcut --> y = ax^2 + bx + c = 0

  1. When a + b + c = 0
    x1 = 1, and x2 = c/a
    Example: y = 3x^2 + 4x - 7 = 0
    x1 = 1, and x2 = - 7/3

  2. When a - b + c = 0.
    x1 = - 1, and x2 = - c/a
    Example. y = 5x^2 + 3x - 2x = 0
    x1 = - 1, and x2 = -c/a = 2/5