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

p^{3} - p x + 6 = 0

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p^{2} - p x + 6 = 0

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p^{2} - 8 p + 7 = 0

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p^{2} - 5 p + 7 = 0

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Solution

The correct option is C $p^{2} - 8 p + 7 = 0$
The solution of $p$ in the form of $(p - 1 (p - 7) = 0$
By multiplying, we get
$p^{2} - 7 p - p + 7 = 0$
Therefore, the quadratic equation is $p^{2} - 8 p + 7 = 0$

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