Question

If the difference of the roots of {{x}^{2}}-px+8=0
be 2, then the value of p is [Roorkee 1992]
A) \pm 2 B) \pm 4 C) \pm 6 D) \pm 8

Answer 1

Hi ,

x² - px + 8 = 0

compare above quadratic equation with

ax² + bx + c = 0 ,

a = 1 , b = - p , c = 8

Let m , n are two roots of the quadratic

equation .

m + n = - b/ a

m + n = p ---( 1 )

mn = 8 -----( 2 )

m - n = 2 ---( 3 ) [ given ]

( m - n )² = 4

( m + n )² - 4mn = 4

p² - 4 × 8 = 4

p² - 32 = 4

p² = 36

p = ± √36

p = ± 6

Therefore ,

Option ( C ) is correct.

I hope this helps you.

: )