Question

Find all values of j for which the quadratic equation 5x²-7x+j=0 has two real solutions. Write your answer as an equality or inequality in terms of j.

Answer 1

The values of j for which the quadratic equation 5x²-7x+j=0 has two real solutions are those for which j is less than 2.45.

Step-by-step explanation:

To find all the values of j for which the quadratic equation 5x²-7x+j=0 has two real solutions, we look at the discriminant of the quadratic formula, which is given by b² - 4ac. For two real solutions to exist, the discriminant must be positive. Therefore, for our equation, the discriminant is (-7)² - 4(5)(j). Simplifying gives us 49 - 20j. For the discriminant to be positive:

49 - 20j > 0

Solving for j, we get:

j < (49/20)

So, the value of j must be less than 2.45 for the quadratic equation to have two real solutions.