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 

Answer 1

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