Multiple choice

Choose the quadratic equation in $p$, whose solutions are $1$ and $7$.

  1. $p^{3}-px + 6 = 0$
  2. $p^{2}-px + 6 = 0$
  3. $p^{2}- 8p + 7 = 0$
  4. $p^{2}-5p + 7 = 0$
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C Correct answer
Explanation

If roots are 1 and 7, the equation is (p-1)(p-7) = 0, which is p^2 - 8p + 7 = 0.

AI explanation

To form a quadratic equation from its roots, we use the factored form where the equation is given by (p minus first root) multiplied by (p minus second root) equals zero. Substituting the roots 1 and 7 gives (p minus 1)(p minus 7) equals zero. Expanding this product yields p squared minus 8p plus 7 equals zero.

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