The nature of the solutions/roots of a quadratic function can be determined from its discriminant.
The discriminant of a quadratic function can be calculated as:
Discriminant = b² - 4ac
Here,
a = coefficient of squared term = -5
b = coefficient of x term = 8
c = constant = - 7
So, the discriminant will be:
Discriminant = 64 - 4(-5)(-7) = - 76
The value of the discriminant is negative. This shows that the given quadratic function has no real solution.
