Roots of quadratic equation $2n^2\,+\,5n\,+\,2\,=\,0$ are
- $\displaystyle\,n\,=\,-8,\,\frac{-1}{2}$
- $\displaystyle\,n\,=\,-2,\,\frac{-1}{5}$
- $\displaystyle\,n\,=\,-2,\,\frac{1}{2}$
- $\displaystyle\,n\,=\,-2,\,\frac{-1}{2}$
Reveal answer
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Correct answer
Explanation
Factor the quadratic equation 2n^2 + 5n + 2 = 0. (2n + 1)(n + 2) = 0. The roots are n = -1/2 and n = -2.
AI explanation
To find the roots of 2n^2 + 5n + 2 = 0 using the factorization method, split the middle term to get 2n^2 + 4n + n + 2 = 0. Factoring by grouping gives 2n(n + 2) + 1(n + 2) = 0, which simplifies to (2n + 1)(n + 2) = 0. Setting each factor to zero yields the roots n = -1/2 and n = -2.