Question

modeling and analyzing quadratic functions: quadratic equations
quadratic formula: ( x = \frac{-b pm sqrt{b^2 - 4ac}}{2a} )
rounded to the nearest hundredth, what is the positive solution to the quadratic equation ( 0 = 2x^2 + 3x - 8 )?
2.00
1.30
3.50
2.89

Explanation:

Step1: Identify a, b, c values

From $2x^2 + 3x - 8 = 0$, $a=2$, $b=3$, $c=-8$

Step2: Calculate discriminant

$\Delta = b^2 - 4ac = 3^2 - 4(2)(-8) = 9 + 64 = 73$

Step3: Apply quadratic formula (positive root)

$x = \frac{-b + \sqrt{\Delta}}{2a} = \frac{-3 + \sqrt{73}}{2(2)}$

Step4: Compute and round

$\sqrt{73} \approx 8.544$, so $x = \frac{-3 + 8.544}{4} = \frac{5.544}{4} = 1.386 \approx 1.39$

Answer:

1.39