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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$\bigcirc$ $a = \frac{1}{2}, b = 3, c = 2$\
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$\bigcirc$ $a = \frac{1}{2}, b = -3, c = -2$\
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$\bigcirc$ $a = \frac{1}{2}, b = 3, c = -2$\
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$\bigcirc$ $a = \frac{1}{2}, b = -3, c = 2$

Explanation:

Step1: Recall Quadratic Form

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

Step2: Compare with Given Equation

The given equation is \( 0 = \frac{1}{2}x^2 - 3x - 2 \) (rewriting to match \( ax^2 + bx + c = 0 \) gives \( \frac{1}{2}x^2 - 3x - 2 = 0 \)).

• For \( ax^2 \): The coefficient of \( x^2 \) is \( \frac{1}{2} \), so \( a = \frac{1}{2} \).
• For \( bx \): The coefficient of \( x \) is \( -3 \), so \( b = -3 \).
• For \( c \): The constant term is \( -2 \), so \( c = -2 \).

Answer:

a = \(\frac{1}{2}\), b = -3, c = -2 (the second option)