Find all the values of j such that the quadratic equation
5x^2+x+4j=0
has no real solutions. Write your answer as an equality or inequality in terms of j.
Use the quadratic formula, and make the discriminant <0.
a=5,b=1,c=4j
so b²-4ac<0
To find the values of j such that the quadratic equation 5x^2 + x + 4j = 0 has no real solutions, we need to determine when the discriminant of the quadratic equation is negative.
The discriminant (D) is given by the formula D = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c = 0.
In this equation, the coefficients are: a = 5, b = 1, and c = 4j.
Substituting the values into the formula, we have:
D = (1)^2 - 4(5)(4j)
= 1 - 80j
= 1 - 80j
For the quadratic equation to have no real solutions, the discriminant D must be negative. Therefore, we can write the inequality:
1 - 80j < 0
Solving this inequality for j, we have:
-80j < -1
j > -1/80
So, the values of j such that the quadratic equation has no real solutions can be written as the inequality j > -1/80.