Question
Find the real solutions of the equation by graphing. –19x3 – 12x2 + 16x = 0
Answers
GPT 3.5
To graph the equation, we can rearrange it into the form:
-19x^3 - 12x^2 + 16x = 0
Factoring out x, we get:
x(-19x^2 - 12x + 16) = 0
Setting each factor equal to zero, we have two possibilities:
x = 0 or -19x^2 - 12x + 16 = 0
Solving the quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/ 2a
For -19x^2 - 12x + 16 = 0, the coefficients are:
a = -19
b = -12
c = 16
Using the quadratic formula, we have:
x = (-(-12) ± √((-12)^2 - 4(-19)(16)))/ (2(-19))
x = (12 ± √(144 + 1216))/ -38
x = (12 ± √1360)/ -38
x = (12 ± 36.9)/ -38
Simplifying further, we get two possible values for x:
x ≈ -1.026 or x ≈ -0.539
Therefore, the real solutions of the equation -19x^3 - 12x^2 + 16x = 0, as found by graphing, are approximately x = -1.026 and x = -0.539.
-19x^3 - 12x^2 + 16x = 0
Factoring out x, we get:
x(-19x^2 - 12x + 16) = 0
Setting each factor equal to zero, we have two possibilities:
x = 0 or -19x^2 - 12x + 16 = 0
Solving the quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac))/ 2a
For -19x^2 - 12x + 16 = 0, the coefficients are:
a = -19
b = -12
c = 16
Using the quadratic formula, we have:
x = (-(-12) ± √((-12)^2 - 4(-19)(16)))/ (2(-19))
x = (12 ± √(144 + 1216))/ -38
x = (12 ± √1360)/ -38
x = (12 ± 36.9)/ -38
Simplifying further, we get two possible values for x:
x ≈ -1.026 or x ≈ -0.539
Therefore, the real solutions of the equation -19x^3 - 12x^2 + 16x = 0, as found by graphing, are approximately x = -1.026 and x = -0.539.