Question

$x_1,x_2$ are the roots of $x^2-3x+a=0$ and $x_3,x_4$ are the roots of $x^2-12x+b=0.$ If $x_1,x_2,x_3,x_4$ form an increasing G.P. then ordered pair (a,b) is :

• A. (1,16)
• B. (2,32)
• C. (2,16)
• D. (1,32)

Answer 1

The correct option is B

(2,32)

Let $x_1=\alpha ,x_2=\alpha \beta ,x_3=\alpha {\beta }^2,x_4=\alpha {\beta }^3.$

Then $\alpha (1+\beta )=3,{\alpha }^2\beta =a,\alpha {\beta }^2(1+\beta )=12$ ,

${\alpha }^2{\beta }^5=b$ . Then ${\beta }^2=4,\beta =2$ as G.P is increasing

Then $\alpha$ = 1 $\therefore$ a = 2, b=32.