Question

Deyuence U DUI LUJ 3-4.1 U a, ß be the roots of the equation x2 - 3x + a = 0 and y, 8 the roots of x2 - 12x + b = 0 and numbers a, b, y, 8 (in this order) form an increasing G.P., then (A) a = 3, b = 12 (B) a = 12, b = 3 (C) a = 2, b = 32 (D) a = 4, b = 16

JEE/Engineering Exams

Maths

Solution

163

1.0 (1 ratings)

( alpha+beta=3 ) ( alpha beta=a )( quad gamma+delta=12 ) ( y delta=b ) ( alpha beta gamma delta-G P ) dr ( alpha x^{2} ) ox ( r^{3} ) ( frac{alpha+beta}{gamma+delta}=frac{beta}{L^{2}} Rightarrow frac{alpha+alpha gamma}{alpha gamma^{2}+alpha gamma^{3}}=frac{1}{4} ) ( frac{d(1+pi)}{d x^{2}(1+k)}=frac{1}{4} Rightarrow frac{x^{2}=4}{sqrt{x}=2} ) ( (-2 ) negle ( alpha+alpha gamma=3 ) ( Rightarrow quad alpha(1+2)=3 quad Rightarrow alpha=1 ) ( a=alpha(alpha gamma)=1(2)=2 ) ( b=alpha gamma^{2} alpha gamma^{3}=alpha^{2} gamma^{5}=1(2)^{5}=32 ) ( therefore quad int begin{array}{l}a=2 b=32end{array} )