For an equation to have two real solutions, its discriminant must be greater than 0.
k<9/40
Practice makes perfect
We will to use the discriminant of the given quadratic equation to find all values of k such that the equation has two real solutions. In the Quadratic Formula, b^2-4ac is the discriminant.
ax^2+bx+c=0 ⇔ x=- b±sqrt(b^2-4ac)/2a
For the equation to have two real solutions, its discriminant must be greater than 0. Let's first identify the values of a, b, and c.
2x^2-3x+5k=0 ⇔ 2x^2+( -3)x+ 5k=0
We see that a = 2, b = - 3, and that c = 5k. Finally, let's set the discriminant greater than 0 and solve the resulting inequality for k.
For values of k less than 940, the equation has two real solutions.
Extra
Further information
If the discriminant is greater than zero, the equation will have two real solutions. If it is equal to zero, the equation will have one real solution. Finally, if the discriminant is less than zero, the equation will have no real solutions.
