Final answer:
The student's question involves finding real number solutions for a cubic polynomial. The quadratic formula can only be used for quadratic equations and not directly for cubic equations, which require different methods to solve. Factoring, synthetic division, or the Rational Root Theorem are possible techniques to find the real roots of a cubic polynomial.
Step-by-step explanation:
The student is seeking help with finding real number solutions for a polynomial equation given by x³ + 9x² + 23x + 15. This is a cubic equation for which there isn't a straightforward formula like the quadratic formula used for second-degree polynomials. However, we can attempt to solve this by factoring or applying numerical methods such as synthetic division or the Rational Root Theorem to approximate the roots.
For an equation of the form ax² + bx + c = 0, one can use the quadratic formula, which is: x = (-b ± √(b² - 4ac)) / (2a). This formula can find the real solutions for x if the discriminant (b² - 4ac) is non-negative. If it is positive, there are two distinct real solutions; if zero, there is one real repeated solution; if negative, then the solutions are complex.