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Question

Given that p and q are the roots of the equation x2ax+b=0 and Dn=pn+qn. Find the value of Dn+1
  1. aDn- bDn-1
  2. bDn
  3. aDn
  4. aDn+ bDn-1
  5. pDn


Solution

The correct option is A aDn- bDn-1

Option (a)

Shortcut: Assumption

Assume a quadratic equation. Let’s take x2+5x6=0.

Thus, a = sum of roots = -5 and b= product of roots = -6

Roots are p = 1 and q=-6

D1=p1+q1 = -5

D0 = 2

D2 = 37

Assume n=1

We need to find Dn+1=D2 = 37

Look in the answer options for 37

Option a is the only one which gives (-5)(-5)-(-6)(2) = 37

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