Question

joline is solving the equation $0 = x^2 - 5x - 4$ using the quadratic formula. which value is the negative real number solution to her quadratic equation? round to the nearest tenth if necessary. quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ -0.7 -5.7 -1 -4

Explanation:

Step1: Identify coefficients

For equation \(x^2 - 5x - 4 = 0\), \(a = 1\), \(b = -5\), \(c = -4\).

Step2: Calculate discriminant

Discriminant \(D = b^2 - 4ac = (-5)^2 - 4\times1\times(-4) = 25 + 16 = 41\).

Step3: Apply quadratic formula

\(x = \frac{-b \pm \sqrt{D}}{2a} = \frac{5 \pm \sqrt{41}}{2}\).

Step4: Find negative solution

\(x_1 = \frac{5 + \sqrt{41}}{2} \approx \frac{5 + 6.4}{2} = 5.7\), \(x_2 = \frac{5 - \sqrt{41}}{2} \approx \frac{5 - 6.4}{2} = -0.7\).

Answer:

\(-0.7\)