Question

3x^2+7x+j=0

Find all values of j for which the quadratic equation has no real solutions.
Write your answer as an equality of inequality in terms of j.

Answer 1

The values of j for which the quadratic equation 3x^2+7x+j=0 has no real solutions are determined by setting the discriminant, which is 49 - 12j, less than zero, resulting in the inequality j > 49/12.

Step-by-step explanation:

To find all values of j for which the quadratic equation 3x^2+7x+j=0 has no real solutions, we need to look at the discriminant of the quadratic equation, which is given by b^2 - 4ac. For the equation to have no real solutions, the discriminant must be negative. In this case, a = 3, b = 7, and c = j.

So our discriminant is:

7^2 - 4(3)(j)
The discriminant equals: 49 - 12j
For no real solutions, the discriminant (49 - 12j) must be less than 0.
49 - 12j < 0
12j > 49
j > 49/12

Therefore, the inequality for j is j > 49/12.

Answer 2

I hope this helps you