Let p be a prime number. The quadratic equation having its roots as factors of p is

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Solution

Q.
Let p be a prime number. The quadratic equation having its roots as factors of p is

1 $x^{2} - p x + p = 0$

2 $x^{2} - (p + 1) x + p = 0$

3 $x^{2} + (p + 1) x + p = 0$

4 $x^{2} - p x + p + 1 = 0$

Ans.
(2)

Factors of $p = p \times 1$

$∴$ $Roots are p and 1 .$

The quadratic equation is:

$x^{2} - (sum of roots) x + product of roots = 0$

$\Rightarrow x^{2} - (p + 1) x + p = 0$

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