Question

which of these would be the correct first step when using the quadratic formula to solve: 2x² - 19x + 24 = 0

Explanation:

Step1: Recall Quadratic Formula

The quadratic formula is \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \) for a quadratic equation \( ax^2 + bx + c = 0 \).

Step2: Identify \( a \), \( b \), \( c \)

For the equation \( 2x^2 - 19x + 24 = 0 \), we have \( a = 2 \), \( b = -19 \), \( c = 24 \).

Step3: Substitute into Formula

Substitute \( a = 2 \), \( b = -19 \), \( c = 24 \) into the quadratic formula. The numerator's first term is \( -b = -(-19) \), the discriminant is \( b^2 - 4ac = (-19)^2 - 4(2)(24) \), and the denominator is \( 2a = 2(2) \). So the correct first step is \( x = \frac{-(-19) \pm \sqrt{(-19)^2 - 4(2)(24)}}{2(2)} \), which matches the first option (top - most) when we check the structure.

Answer:

The top - most option (with \( x=\frac{-(-19)\pm\sqrt{(-19)^2 - 4(2)(24)}}{2(2)} \))