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:

• \( ax^2 \) is the quadratic term, \( a \) is the leading coefficient (coefficient of \( x^2 \)).
• \( bx \) is the linear term, \( b \) 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 false.
• For the leading coefficient: The coefficient of \( x^2 \) is \( 8 \), so the leading coefficient is \( 8 \). The option saying leading coefficient is \( -5 \) is false (since \( -5 \) is the coefficient of \( x \), the linear term).

Answer:

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