# Determine the number of real solutions of

sciencesolve | Teacher | (Level 3) Educator Emeritus

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The problem is not complete since it does not provide the equation whose number of real solutions needs to be determined.

Supposing that you need to determine the number of real solutions of a quadratic equation `ax^2 + bx + c = 0` , hence, you need to remember the following rules, such that:

- if `Delta = b^2 - 4ac > 0` , the equation has two different real solutions

- if `Delta = 0` , the equation has two real solutions, that have equal values

- if Delta < 0, the equation has two imaginary solutions

You should remember that the number of real solutions depends on the number of complex solutions since the complex solutions come in pairs.

Considering as example the third order polynomial `ax^3 + bx^2 + cx + d = 0` can either have all three real solutions, or two imaginary solutions and one real. You should notice that the number of solutions, real or imaginary, cannot be larger than the maximum degree of polynomial.