The roots of the equation $2{x}^{2}+x-4=0$ are
- $1,-4$
- $-3,\cfrac {1}{\sqrt {3}}$
- $\cfrac{\sqrt {33}-1}{4},\cfrac{-\sqrt {33}-1}{4}$
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None
Reveal answer
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C
Correct answer
Explanation
Using the quadratic formula x = (-b +/- sqrt(b^2 - 4ac)) / 2a for 2x^2 + x - 4 = 0, where a=2, b=1, c=-4. The discriminant is 1^2 - 4(2)(-4) = 1 + 32 = 33. The roots are (-1 +/- sqrt(33)) / 4.
AI explanation
Using the quadratic formula, x = [-b ± sqrt(b^2 - 4ac)] / 2a, with a = 2, b = 1, and c = -4. Calculate the discriminant as (1)^2 - 4(2)(-4) = 1 + 32 = 33. Substituting these values gives x = [-1 ± sqrt(33)] / 4, which simplifies to the two roots (sqrt(33) - 1)/4 and (-sqrt(33) - 1)/4.