Question

for a quadratic function, the solution is $x = \frac{-8 \pm \sqrt{8^2 - 4(2)(-3)}}{4}$. which of the following is one of the solutions rounded?

a 24

b -6.312

c 5.482

d this has no real solutions.

e -4.812

Explanation:

Step1: Calculate the discriminant

First, calculate the value inside the square root (the discriminant): \( b^2 - 4ac \) where \( a = 2 \), \( b = 9 \), \( c = -3 \). So, \( 9^2 - 4(2)(-3) = 81 + 24 = 105 \).

Step2: Calculate the square root

Find \( \sqrt{105} \approx 10.247 \).

Step3: Calculate the two solutions

First solution: \( \frac{-9 + 10.247}{4} = \frac{1.247}{4} \approx 0.312 \) (Wait, no, maybe I made a mistake. Wait, original formula: \( x = \frac{-9 \pm \sqrt{9^2 - 4(2)(-3)}}{4} \). Wait, \( 9^2 - 4(2)(-3) = 81 + 24 = 105 \), so \( \sqrt{105} \approx 10.24695 \). Then first solution: \( \frac{-9 + 10.24695}{4} = \frac{1.24695}{4} \approx 0.3117 \) (not matching options). Second solution: \( \frac{-9 - 10.24695}{4} = \frac{-19.24695}{4} \approx -4.8117 \approx -4.812 \).

Answer:

E. -4.812