6
QuizMultiple Choice

Quadratics and Complex Numbers — Test

Question 6 • Algebra II

Which statement about the following equation is true? 3 x squared minus 8 x plus 5 is equal to 5 x squared

Answer
A
The discriminant is greater than 0 , so there are two complex roots.
B
The discriminant is less than 0 , so there are two real roots.
C
The discriminant is greater than 0 , so there are two real roots.
D
The discriminant is less than 0 , so there are two complex roots.

Explanation

Move all terms to one side: 3x² − 8x + 5 = 5x² becomes 2x² + 8x − 5 = 0. Its discriminant is b² − 4ac = 8² − 4(2)(−5) = 104, which is greater than 0. Therefore, the equation has two distinct real roots, so the true statement is “The discriminant is greater than 0, so there are two real roots.”

AI-written and checked against the verified answer.

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