If 3x^2 + 2x + k = 0 Find k

Question

if: i) roots are equal in absolute value and opposite in sign. ii) the roots are real and different. 

Answer 1

The equation 3x² + 2x + k = 0

Compare it to quadratic equation ax² + bx + c = 0

a = 3, b = 2, c = k

ii) If discriminant is positive then the roots are real and different.

b² - 4ac > 0

2² - 4(3)(k) > 0

4 - 12k > 0

4 > 12k

4/12 > k

1/3 > k

Solution k < 1/3

Answer 2

The equation 3x² + 2x + k = 0

Compare it to quadratic equation ax² + bx + c = 0

a = 3, b = 2, c = k

i) If the discriminant is zero then the roots are equal.

b² - 4ac = 0

2² - 4(3)(k) = 0

4 - 12k = 0

4 = 12k

Solution k = 1/3.