Question

The value of p for which roots of the quadratic equation x² – px + 6 = 0 are rational, is ______.

Options

• 1

• –5

• 25

• `sqrt(5)`

Answer 1

The value of p for which roots of the quadratic equation x² – px + 6 = 0 are rational, is –5.

Explanation:

Given equation: x² – px + 6 = 0

For the roots to be rational, the discriminant (D) must be a perfect square.

D = b² – 4ac

D = (–p)² – 4(1)(6)

D = p² – 24

Checking options:

(A) If p = 1,

D = 1² – 24

= –23 (Not a perfect square)

(B) If p = –5,

D = (–5)² – 24

= 25 – 24

= 1 (Perfect square)

(C) If p = 25,

D = 25² – 24

= 625 – 24

= 601 (Not a perfect square)

(D) If `p = sqrt(5)`, 

`D = (sqrt(5))^2 - 24`

= 5 – 24

= –19 (Not a perfect square)

Since D = 1 is a perfect square for p = –5, the roots are rational.