Find the roots of the quadratic equation by applying the quadratic formula $\displaystyle 2x^2 + x - 4 = 0$
- $\displaystyle \frac{1 \pm \sqrt {33}}{4}$
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$\displaystyle \frac{-1 \pm \sqrt {33}}{4}$
- $\displaystyle \frac{1 \pm \sqrt {31}}{4}$
- $\displaystyle \frac{-1 \pm \sqrt {31}}{4}$
For 2x^2 + x - 4 = 0, a=2, b=1, c=-4. The quadratic formula is x = (-b +/- sqrt(b^2 - 4ac)) / 2a. x = (-1 +/- sqrt(1^2 - 4*2*(-4))) / (2*2) = (-1 +/- sqrt(1 + 32)) / 4 = (-1 +/- sqrt(33)) / 4.
Using the quadratic formula x equals the quantity negative b plus or minus the square root of (b squared minus 4ac) all divided by 2a, we identify a equals 2, b equals 1, and c equals negative 4 for the equation 2x squared plus x minus 4 equals 0. Substituting these into the formula gives x equals (negative 1 plus or minus the square root of (1 squared minus 4(2)(negative 4))) divided by 2(2). The value inside the square root simplifies to 1 plus 32, which is 33. The final result is x equals the quantity negative 1 plus or minus the square root of 33 all divided by 4.