Question

Given that p and q are the roots of the equation $x^2-ax+b=0$ and $D_n=p^n+q^n$. Find the value of $D_{n+1}$

• A. aD_n- bD_n-1
• B. aD_n
• C. bD_n
• D. aD_n+ bD_n-1
• E. pD_n

Answer 1

The correct option is A aD_n- bD_n-1

Option (a)

Shortcut: Assumption

Assume a quadratic equation. Let’s take $x^2+5x-6=0$.

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

Roots are p = 1 and q=-6

$D_1=p^1+q^1$ = -5

$D_0$ = 2

$D_2$ = 37

Assume n=1

We need to find $D_{n+1}=D_2$ = 37

Look in the answer options for 37

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