Question

rounded to the nearest hundredth, what is the positive solution to the quadratic equation 0=2x²+3x-8?
quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$
\bigcirc 1.39
\bigcirc 2.00
\bigcirc 2.89
\bigcirc 3.50

Explanation:

Step1: Identify coefficients

For equation \(2x^2 + 3x - 8 = 0\), \(a = 2\), \(b = 3\), \(c = -8\).

Step2: Apply quadratic formula

\(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}=\frac{-3\pm\sqrt{3^2 - 4\times2\times(-8)}}{2\times2}=\frac{-3\pm\sqrt{9 + 64}}{4}=\frac{-3\pm\sqrt{73}}{4}\).

Step3: Calculate positive solution

\(\sqrt{73}\approx8.544\), so \(x=\frac{-3 + 8.544}{4}=\frac{5.544}{4}=1.386\approx1.39\).

Answer:

1.39