Question

what are the zeros of the polynomial function ( g(x) = x^2 - 5x + 6 )?
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the zeros of the function are ( x = square ) and ( x = square )

Explanation:

Step1: Factor the polynomial

To find the zeros of \( g(x) = x^2 - 5x + 6 \), we factor the quadratic. We need two numbers that multiply to \( 6 \) and add to \( -5 \). Those numbers are \( -2 \) and \( -3 \). So, \( g(x)=(x - 2)(x - 3) \).

Step2: Set each factor to zero

To find the zeros, we set each factor equal to zero:

• For \( x - 2 = 0 \), solving gives \( x = 2 \).
• For \( x - 3 = 0 \), solving gives \( x = 3 \).

Answer:

The zeros of the function are \( x = 2 \) and \( x = 3 \).