Question

If $( n +3)^2= a ( n +2)^2+ b ( n +1)^2+ cn ^2$ holds true for every positive integer $n$ then the quadratic equation $ax ^2+ bx + c =0$ has

• A. both positive roots
• B. both negative roots
• C. one positive and one negative root
• D. no real roots.

Answer 1

Answer: (D)

$a =3 ; b =-3 \text { and } c =1 $
$\therefore 3 x ^2-3 x +1=0$
$D <0 \Rightarrow \text { no real roots }$