Question

Find the value of k for which the difference between the root of the equation x2+kx+8=0 is 2

Answer 1

Answer:

Step-by-step explanation:

$Let\:the\:roots\:be\:\alpha\:and\:\beta$

Given:

$\alpha-\beta=2$

$\alpha+\beta=-k$

$\alpha\beta=8$

${(\alpha-\beta)}^2={(\alpha+\beta)}^2-4\alpha\beta$

$4={k}^2-4(8)\\4={k}^2-32\\{k}^2=36$

k=6, -6

Answer 2

Answer to the question,

Given the equation,

x²+kx+8=0

By comparing with ax²+bx+c, we get

a=x; b=k; c=8

Let, α and β be the roots of the equation.

Sum of the roots, α+β=-b/a=-k/1=-k

Product of the roots, α.β=c/a=8/1=8

And,  α-β=2 ( given in the question )

Now,

(α-β)²=(α+β)²-4αβ

⇒ 2²=(-k)²-4×8

⇒ 4=k²-32

⇒ 4+32=k²

⇒ 36=k²

⇒ k²=32

⇒ k=±√36

⇒ k= ±√2×2×3×3

⇒ k=±2×3

⇒ k=±6

So, the answer is ±6 or -6,6