Final answer:
The solution to the equation 7x² + 3x - j = 0 is found using the quadratic formula, resulting in x = (-3 ± √(9 + 28j) ) / 14 in terms of j. This allows us to express the roots of the quadratic equation depending on the value of j.
Step-by-step explanation:
To solve the equation 7x² + 3x - j = 0 for x in terms of j, we will use the quadratic formula. The quadratic formula states that for any quadratic equation of the form ax² + bx + c = 0, the solution for x is given by:
x = ∓( -b ± √(b² - 4ac) ) / (2a)
Applying this formula to the given equation where a = 7, b = 3, and c = -j, we get:
x = (-3 ± √(3² - 4 × 7 × (-j) ) ) / (2 × 7)
x = (-3 ± √(9 + 28j) ) / 14
This is the solution to the equation in terms of j.
After finding the value of x, always eliminate terms wherever possible to simplify the algebra, and check the answer to see if it is reasonable.