Question

Which statement best describes the equation (x + 5)2 + 4(x + 5) + 12 = 0?
The equation is quadratic in form because it can be rewritten as a quadratic equation with u substitution u = (x + 5).
The equation is quadratic in form because when it is expanded, it is a fourth-degree polynomial.
The equation is not quadratic in form because it cannot be solved by using the quadratic formula.
The equation is not quadratic in form because there is no real solution.

Answer 1

"The equation is quadratic in form because it can be rewritten as a quadratic equation with u substitution u = (x + 5)."

Reason: Let u = x + 5. Then the equation becomes u^2 + 4u + 12 = 0, which is a quadratic in u (though its discriminant 4^2 − 4·1·12 = −32 < 0, so the roots are complex).