3x^2+5x+4 = 0
Let's now use the discriminant of the equation to determine the type of solutions. In the Quadratic Formula, b^2-4ac is the discriminant.
ax^2+bx+c=0
⇕
x=- b±sqrt(b^2-4ac)/2a
If we just want to know the type of the solutions, and not the solutions themselves, we only need to work with the discriminant. Since the equation is already in standard form, we can identify the values of a, b, and c.
3x^2+ 5x+ 4=0
Finally, let's evaluate the discriminant.
Since the discriminant is -23, the quadratic equation has two complex 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 roots.
b We want to determine whether the given quadratic function has real or complex roots. To do so, we need to consider the following quadratic equation.
3x^2+5x-4 = 0
Let's now use the discriminant of the equation to determine the type of solutions. In the Quadratic Formula, b^2-4ac is the discriminant.
ax^2+bx+c=0
⇕
x=- b±sqrt(b^2-4ac)/2a
If we just want to know the type of the solutions, and not the solutions themselves, we only need to work with the discriminant. Since the equation is already in standard form, we can identify the values of a, b, and c.
3x^2+5x-4=0
⇕
3x^2+ 5x+( -4)=0
Finally, let's evaluate the discriminant.
Since the discriminant is 73, the quadratic equation has two real solutions. Therefore, the function has real roots.
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.
