Classify the quadratic equation based on the number of solutions

QUESTION 1

The given equation is



We rewrite in the form,



This implies that,





We can use the determinant to find the number of solutions without necessarily solving the equation.









Since the determinant is negative the equation



has no solution.

QUESTION 2

The given equation is













Since the determinant is positive, the equation



has two solutions.

QUESTION 3

The given equation is



This implies that,







The determinant is





Since the determinant is negative, the equation


has no solution.

QUESTION 4

The given equation is



We rewrite to obtain,





The determinant is







Since the determinant is positive the equation



has two solutions.

QUESTION 5

The given equation is



We rewrite to obtain,





We substitute in the determinant formula to obtain,



.




Since the determinant is zero the equation


has only one root.