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Question
Let p be a prime number. The quadratic equation having its roots as factors of p is ______.
Options
x2 – px + p = 0
x2 – (p + 1)x + p = 0
x2 + (p + 1)x + p = 0
x2 – px + p + 1= 0
Solution
Let p be a prime number. The quadratic equation having its roots as factors of p is `underline(bb(x^2 - (p + 1)x + p = 0)`.
Explanation:
Since p is a prime factor
Factors of p = 1, p
Thus, we need to find quadratic equation with roots 1 and p
Required quadratic equation is x2 – (Sum of roots)x + Product of roots = 0
x2 – (1 + p)x + (1 × p) = 0
x2 – (1 + p)x + p = 0
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