Question

rhett is solving the quadratic equation 0= x² - 2x - 3 using the quadratic formula. which shows the correct substitution of the values a, b, and c into the quadratic formula?
quadratic formula: x = (-b ± √(b² - 4ac))/(2a)
options:

1. (2 ± √((-2)² - 4(1)(-3)))/(2(1))
2. (-2 ± √((-2)² - 4(1)(-3)))/(2(1))
3. (2 ± √(-2² - 4(1)(-3)))/(2(1))
4. (-2 ± √(-2² - 4(1)(-3)))/(2(1))

Explanation:

Step1: Identify a, b, c

For quadratic equation \(ax^2 + bx + c = 0\), given \(0 = x^2 - 2x - 3\) (or \(x^2 - 2x - 3 = 0\)), so \(a = 1\), \(b = -2\), \(c = -3\).

Step2: Substitute into quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\). Substitute \(a = 1\), \(b = -2\), \(c = -3\):
\(-b=-(-2)=2\), \(b^2 = (-2)^2\), \(4ac = 4(1)(-3)\), \(2a = 2(1)\).
So substitution is \(\frac{2\pm\sqrt{(-2)^2 - 4(1)(-3)}}{2(1)}\).

Answer:

\(\boldsymbol{\frac{2\pm\sqrt{(-2)^2 - 4(1)(-3)}}{2(1)}}\) (the first option)