Final answer:
The quadratic equation bx²+3x+2=0 will have more than one real solution if the discriminant (b² - 4ac) is positive. After evaluating the discriminant for each value of b, the equation has more than one real solution for b=1 and b=-2.
Step-by-step explanation:
To determine for which values of b the quadratic equation bx²+3x+2=0 will have more than one real solution, we must look at the equation's discriminant, which is found using the formula b² - 4ac. In this context, a is the coefficient of x² (which is b), b is the coefficient of x (which is 3), and c is the constant term (which is 2).
A quadratic equation will have more than one real solution if the discriminant is positive, which means b² - 4ac > 0. Let's analyze the discriminant for each given value of b:
- For b=1: (3² - 4(1)(2)) = 9 - 8 = 1. Since 1 is positive, there will be more than one real solution.
- For b=-2: (3² - 4(-2)(2)) = 9 - (-16) = 25. Since 25 is positive, there will be more than one real solution.
- For b=0: The equation becomes linear (3x + 2 = 0), so it only has one solution.
- For b=3: (3² - 4(3)(2)) = 9 - 24 = -15. Since -15 is negative, there will be no real solutions.
Therefore, the quadratic equation will have more than one real solution for b=1 and b=-2.