Roots of quadratic equation $7p^2\,-\,5p\,-\,2\,=\,0$ are
- $\displaystyle\,p\,=\,3,\,\frac{-2}{7}$
- $\displaystyle\,p\,=\,2,\,\frac{-2}{7}$
- $\displaystyle\,p\,=\,1,\,\frac{-2}{7}$
- $\displaystyle\,p\,=\,1,\,\frac{2}{7}$
Reveal answer
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C
Correct answer
Explanation
7p^2 - 5p - 2 = 0. Using the quadratic formula or factoring: 7p^2 - 7p + 2p - 2 = 0 -> 7p(p-1) + 2(p-1) = 0 -> (7p+2)(p-1) = 0. Roots are p = 1 and p = -2/7.
AI explanation
Using the factorization method, split the middle term of 7p^2 - 5p - 2 = 0 to get 7p^2 - 7p + 2p - 2 = 0. Factoring by grouping gives 7p(p - 1) + 2(p - 1) = 0, which simplifies to (7p + 2)(p - 1) = 0. Setting each factor to zero yields the roots p = -2/7 and p = 1.