Question

Let a and b be roots of $x^2-3x+p=0$ and let c and d be roots of $x^2-12x+q=0$ where a,b,c,d form increasing G.P. then the ratio of (q + p) : (q - p) is equal to

Answer 1

$a+b=3$ $c+d=12$

Let $G.P\to a,ar,a{r}^2,a{r}^3$

$a(1+r)=3a{r}^3+a{r}^3=12$

$a{r}^2(1+r)=12$

$r^2=4$

$r=2$ (Increasing $G.P$)

$\therefore a=1$

Roots are $1,2,4,8$

$P=1\times 2=2$ $q=4\times 8=32$

$\frac{q+p}{q-p}=\frac{32+3}{32-2}=\frac{34}{30}=17:15$