Latest IBM Aptitude Question SOLUTION: If the ratio of the roots of the equation x2 – 2ax + b = 0 is equal to that of the roots x2 – 2cx + d = 0, then: a) a2b = c2 d b) a2c = b2d b) a2d = c2b d) d2 b = c

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(#M40154974) IBM Numerical Ability question Keep an EYE

If the ratio of the roots of the equation x2 – 2ax + b = 0 is equal to that of the roots x2 – 2cx + d = 0, then:
a) a2b = c2 d b) a2c = b2d
b) a2d = c2b d) d2 b = c2 a

Asked In IBM neha (8 years ago)

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Jaydev Dinda  (8 years ago)

x^2-2ax+b=0 for this eqn..roots r....R1=2a/1,R2=b/1;
x^2-2cx+d=0 for this eqn ..roots r...R3=2c/1,R4=d;
As per question ,2a/b=2c/d
=>2ad=2bc (Option b)ans

Is this solution Helpfull? Yes (17) | No (10)  

arif mirza  (8 years ago)

answer is C

roots for 1st equation will be (a+√a^2-b)/a & (a-√a^2-b)/a

similarly for 2nd equation roots will be (c+√c^2-d)/c & (c-√c^2-d)/c

now according to the qsn, ratio of roots are equal, so after solving few steps we will get relation as:

(a+√a^2-b)/(a-√a^2-b) = (c+√c^2-d)/(c-√c^2-d)

now apply Componendo et Dividendo

we will get

a/(√a^2-b) = c/(√c^2-d)

squaring both side,

a^2/(a^2-b) = c^2/(c^2-d)

= a^2c^2 - a^2d = a^2c^2 - bc^2

= a^2d = c^2b -------------- C)

Is this solution Helpfull? Yes (9) | No (5)  

jp   (8 years ago)

a is right solution
because a=c,b=d
hence a2b=c2d

Is this solution Helpfull? Yes (3) | No (8)  

Mamatha Turerao  (8 years ago)

x = a ab ± 2 – = a ab + 2 – and a ab − 2 –
and y = c cd ± 2 – = c cd + 2 – and c cd − 2 –
a ab
aab
+ −2
2 – –
= c cd
c cd
+ −2
2 – –
By reversing componendo and dividendo,
a
a b 2 −
= c
c d 2 −
Squaring, a
a b
2
2 – = c
c d
2
2 – , i.e. a2
d = bc2

Is this solution Helpfull? Yes (2) | No (2)  

Kerwin Wang  (8 years ago)

if a = 1, b = 15, the roots for the first equation would be 3 and -5; thus if we make the roots of the second equation -6 and 10 maintaining the -3/5 ratio, we would have c = 2, d = 60. Thus finally a^2 = 1 b = 15 c^2 =4 and d = 60, making b the answer.

Is this solution Helpfull? Yes (1) | No (5)  

ankita patil  (8 years ago)

a2d=c2b
because d and b

Is this solution Helpfull? Yes (1) | No (2)  

swati  (7 years ago)

let roots of 1st eq. be m,n and roots of 2nd eq. be u,i
now, sum of roots m+n=-(-2a)/1=>2a and
sum of roots u+i=-(-2c)/1=>2c
a/q .....
m/n=u/i
m/n+1=u/i+1
(m+n)/n=(u+i)/i
2a/n=2c/i
hence a/c=n/i.....(1)
also...
product of roots mn=b
and ui=d
as m/n=u/i
b/n^2=d/i^2
hence b/d=(n/i)^2.....(2)
using 1 and 2 we get
(a/c)^2=b/d
hence a^2d=c^2b
so option b is correct

Is this solution Helpfull? Yes (1) | No   

Rakesh Thota  (8 years ago)

ans b
a=c
c=d

Is this solution Helpfull? Yes | No (6)  

Aluri Saieesh Kumar  (8 years ago)

a=c;
b=d because
by equating coefficients

Is this solution Helpfull? Yes | No (1)  

Olga  (8 years ago)

b
just solve the equation

Is this solution Helpfull? Yes | No (2)  

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