If the value of the discriminant of a particular quadratic equation is 45, describe the nature of the solution(s).

A. Two real, rational solutions
Incorrect. 45 is not a perfect square therefore the solutions will not be rational.

B. One (double) real solution
Incorrect. The discriminant would have to be zero.

C. Two real, irrational solutions
Correct! 45 is not a perfect square therefore there are two real, irrational solutions.

D. Two complex (imaginary) solutions
Incorrect. 45 is positive, the solutions would not be complex.

If the value of the discriminant of a particular quadratic equation is -64, describe the nature of the solution(s).

A. Two real, rational solutions
Incorrect. √-64 is not real.

B. One (double) real solution
Incorrect. The discriminant isn’t zero.

C. Two real, irrational solutions
Incorrect. √-64 is not real.

D. Two complex (imaginary) solutions
Correct! √-64 is imaginary.

Find the value of the discriminant for the following quadratic equation and describe the nature of the solution(s): 2x² + 3x − 2 = 0

1. D = -7; two complex solutions
2. D = 25; two real, rational solutions
3. D = 7; two real, irrational solutions
4. D = 25; one real, rational solution

A
Incorrect. Check your signs, the second value is positive.

B
Correct! √(3²-4(2)(-2))=√25 = 5, which is rational.

C
Incorrect. Check your addition, the both values are positive.

D
Incorrect. The discriminant is the perfect square 25 therefore there are two real, rational solutions.

Which of the following possible discriminant values would yield two real, irrational solutions?

A. 64
Incorrect. Two real, rational solutions. √64 is rational.

B. 24
Correct! √24 is irrational, therefore 2 irrational solutions.

C. -24
Incorrect. √-24 is imaginary.

D. -64
Incorrect. √-64 is imaginary.