Question

what are the values of a, b, and c in the quadratic equation $0 = \frac{1}{2}x^2 - 3x - 2$?\
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$\circ$ $a = \frac{1}{2}, b = 3, c = 2$\
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$\circ$ $a = \frac{1}{2}, b = -3, c = -2$\
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$\circ$ $a = \frac{1}{2}, b = 3, c = -2$\
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$\circ$ $a = \frac{1}{2}, b = -3, c = 2$

Explanation:

Step1: Recall quadratic form

The standard quadratic equation is \( ax^2 + bx + c = 0 \), where \( a \), \( b \), \( c \) are coefficients.

Step2: Match given equation

Given equation: \( 0=\frac{1}{2}x^2 - 3x - 2 \), rewrite as \( \frac{1}{2}x^2 - 3x - 2 = 0 \).
Compare with \( ax^2 + bx + c = 0 \):

• \( a=\frac{1}{2} \) (coefficient of \( x^2 \)),
• \( b = -3 \) (coefficient of \( x \)),
• \( c = -2 \) (constant term).

Answer:

B. \( a=\frac{1}{2}, b=-3, c=-2 \)