Question

which statement is true about the quadratic equation $8x^2 - 5x + 3 = 0$?

• the constant term is 8.
• the constant term is -5.
• the leading coefficient is 8.
• the leading coefficient is -5.

Explanation:

Step1: Recall Quadratic Equation Structure

A quadratic equation is in the form \( ax^2 + bx + c = 0 \), where:

• \( a \) is the leading coefficient (coefficient of \( x^2 \)),
• \( b \) is the coefficient of \( x \),
• \( c \) is the constant term (term without \( x \)).

Step2: Analyze Given Equation \( 8x^2 - 5x + 3 = 0 \)

• For the constant term: The term without \( x \) is \( 3 \), so options about constant term being \( 8 \) or \( -5 \) are wrong.
• For the leading coefficient: The coefficient of \( x^2 \) is \( 8 \), so the leading coefficient is \( 8 \). The coefficient of \( x \) is \( -5 \), not the leading coefficient.

Answer:

The leading coefficient is 8. (Corresponding option: The option stating "The leading coefficient is 8.")