Question

How many and what type of solutions does each quadratic have?

1. 3x^2-4x+11=0 2. 2x^2-4x+2=0 3. 2x^2-3x-9=0

Answer 1

The number and type of solutions for each quadratic equation can be determined by analyzing the discriminant.

Step-by-step explanation:

The type and number of solutions of a quadratic equation can be determined by analyzing the discriminant, which is the expression inside the square root of the quadratic formula.

1. For the equation 3x^2-4x+11=0, the discriminant is -80. Since the discriminant is negative, the quadratic has two complex solutions.
2. For the equation 2x^2-4x+2=0, the discriminant is 0. Since the discriminant is equal to zero, the quadratic has one real solution.
3. For the equation 2x^2-3x-9=0, the discriminant is 45. Since the discriminant is positive, the quadratic has two real solutions.