NIMCET 2019 Question Paper with solutions

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Question : 10 of 120

Marks: +1, -0

If a,

a_1, a_2, a_3

,....,

a_{2n-1}

, b are in AP, a, b,

b_1, b_2, b_3

,....,

b_{2n-1}

are in GP and a,

c_1, c_2, c_3

,

c_{2n-1}

, b are in HP, where a, b are positive, then the equation

a_nx^2

-

b_n

x +

c_n

= 0 has its roots

Real and equal
Real and unequal
Imaginary
One real and one imaginary

Solution:

Given

a,a_1,a_2,a_3,a_4.....a_{2n-1}

, b are in A.P

a,b_1,b_2,b_3,b_4,b...b_{2n-1}

are in G.P

a,c_1,c_2,c_3,...,c_{2n-1}

are in H.P

a_n={a+b}/2⇒b_n=√{ab}

c_n={2ab}/{a+b}

Now,

a_nx^2-b_nx+c_n=0

D=(b_n)^2-4a_nc_n

D=ab-4{(a+b)}/2{2(ab)}/{a+b}

D=ab-4ab

D=-3ab < 0

∴ Roots are imaginary.

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