Question

If
$\alpha$
and
$\beta$
are the roots of the equation
${x}^{2} - px - 1 = 0$
then,
${( \alpha - \beta )}^{2}$
is?

Answer 1

Answer:

p²- 2

Step-by-step explanation:

Given Equation is x² - px - 1 = 0.

On comparing with ax² + bx + c = 0, we get

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

Given that α,β are the roots of the equation.

(i) Sum of roots:

α + β = -b/a

         = -(-p)/1

         = p.

(ii) Product of roots:

αβ = c/a

     = -1/1

     = -1.

Now,

Given Equation is (α - β)² = (α + β)² - 4αβ

                                          = (p)² - 4(-1)

                                          = p² + 4

Hope it helps!