Question

use the quadratic formula to solve the quadratic equation $2x^2 - 3x - 4 = 0$. separate multiple solutions with commas if necessary.
x =

Explanation:

Step1: Identify coefficients

For \(2x^2 - 3x - 4 = 0\), \(a = 2\), \(b = -3\), \(c = -4\).

Step2: Apply quadratic formula

Quadratic formula: \(x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a}\).
Substitute values:
\(x=\frac{-(-3)\pm\sqrt{(-3)^2 - 4(2)(-4)}}{2(2)}\)
Simplify inside sqrt:
\((-3)^2 - 4(2)(-4)=9 + 32 = 41\)
So, \(x=\frac{3\pm\sqrt{41}}{4}\).

Answer:

\(\frac{3 + \sqrt{41}}{4},\frac{3 - \sqrt{41}}{4}\)