Multiple choice

Roots of quadratic equation $7p^2\,-\,5p\,-\,2\,=\,0$ are

  1. $\displaystyle\,p\,=\,3,\,\frac{-2}{7}$
  2. $\displaystyle\,p\,=\,2,\,\frac{-2}{7}$
  3. $\displaystyle\,p\,=\,1,\,\frac{-2}{7}$
  4. $\displaystyle\,p\,=\,1,\,\frac{2}{7}$
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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.