16
QuizMultiple Choice

Transformations of Quadratic Functions — Unit test

Question 16 • FL-1200330-Algebra 2 CR

Which statement about the following equation is true?3x2 – 8x + 5 = 5x2

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

Explanation

Put the equation in standard form by subtracting 5x² from both sides: −2x² − 8x + 5 = 0, or equivalently 2x² + 8x − 5 = 0. Here a = 2, b = 8, and c = −5, so the discriminant is b² − 4ac = 8² − 4(2)(−5) = 104. Since 104 is greater than 0, the equation has two real roots. The true statement is “The discriminant is greater than 0, so there are two real roots.”

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