Question

If the difference between of the roots of the equation x^2-px+8=0is2 then the value of p is

Answer 1

Answer:

±6

Step-by-step explanation:

Let one root be α

Then other will be α-2

α(α-2)=8/1

α=4,-2

So, roots are 4,2 or -2,-4

(4+2)=-(-p)

p=6

or

p=(-6)

Answer 2

Step-by-step explanation:

Given equation :

x² + px + 8 = 0 .....(i)

Let, α and β are roots of (i).

Then,

α + β = - p .....(ii)

and

αβ = 8 .....(iii)

Given :

α - β = 2

=> (α - β)² = 2²

=> (α + β)² - 4αβ = 4

=> p² - (4 × 8) = 4

=> p² - 32 = 4

=> p² = 32 + 4 = 36 = 6²

=> p = ± 6

So, the required values of p are

p = ± 6.