Question

If the difference between the roots of the equation x²+px+8=0 is 2,then p= is 2,-4,4,-2

Answer 1

Step-by-step explanation:

The difference of the roots

$\sqrt{ {p}^{2} - 32} = 2 \: (given)$

So we get,

${p}^{2} - 32 = 4$

${p}^{2} = 32 + 4 = 36$

$p = \sqrt{36} = + - 6$

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.