Which expression represents the quadratic equation in standard form?

Which expression represents the quadratic equation in standard form?

• A. x^2 + 5 = 0
• B. 2x^2 + 3x + 1 = 0
• C. 3x - 2 = 0
• D. x^2 - 4 = 0

Answer: (B)

To determine which expression represents a quadratic equation in standard form, it's essential to understand what standard form for a quadratic equation is. A quadratic equation is typically expressed as \( ax^2 + bx + c = 0 \), where \( a \), \( b \), and \( c \) are constants, and \( a \) must be non-zero. The expression that correctly fits this definition is \( 2x^2 + 3x + 1 = 0 \). In this expression: - The term \( 2x^2 \) represents the quadratic term, where \( a = 2 \). - The term \( 3x \) represents the linear term, where \( b = 3 \). - The constant term \( 1 \) represents \( c \). Thus, it clearly conforms to the required structure of a quadratic equation in standard form. In contrast, the other expressions do not fit the standard form of a quadratic equation. For instance, the expression \( x^2 + 5 = 0 \) is a quadratic equation but lacks a linear term. The expression \( 3x - 2 = 0 \) is linear, not quadratic, and therefore does not contain an \(

To determine which expression represents a quadratic equation in standard form, it's essential to understand what standard form for a quadratic equation is. A quadratic equation is typically expressed as ( ax^2 + bx + c = 0 ), where ( a ), ( b ), and ( c ) are constants, and ( a ) must be non-zero.

The expression that correctly fits this definition is ( 2x^2 + 3x + 1 = 0 ). In this expression:

• The term ( 2x^2 ) represents the quadratic term, where ( a = 2 ).

• The term ( 3x ) represents the linear term, where ( b = 3 ).

• The constant term ( 1 ) represents ( c ).

Thus, it clearly conforms to the required structure of a quadratic equation in standard form.

In contrast, the other expressions do not fit the standard form of a quadratic equation. For instance, the expression ( x^2 + 5 = 0 ) is a quadratic equation but lacks a linear term. The expression ( 3x - 2 = 0 ) is linear, not quadratic, and therefore does not contain an (