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. aDn ₊ bD_n-1

Answer 1

The correct option is A aD_n-bD_n-1

Best way to proceed is by assumption of values.

Assume a quadratic equation. Let’s take $x^2+5x-6=0$. Here the roots are p =1 and q =-6

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