If the square of the roots of the equation x^2 - 3ax + a^2 = 0, find a

Question

The square of the roots of the equation  x^2 - 3ax + a^2 = 0  is 1.75 and a>0. Find a.

A. 0.5
B. 0.7
C. 0.75
D. 0.9
E. 1.25

chetan2u · Answer

'The square of the roots of the equation  x^2 - 3ax + a^2 = 0  is 1.75' does not make sense and should be 
 The SUM OF THE square of the roots of the equation  x^2 - 3ax + a^2 = 0  is 1.75

Let the two roots be  x_1  and  x_2 
So,  x_1^2+x_2^2=1.75 
 x_1^2+x_2^2+2x_1x_2-2x_1x_2=1.75 
 (x_1+x_2)^2-2x_1x_2=1.75

Sum of the roots = 3a
product of the roots = a^2

(x_1+x_2)^2-2x_1x_2=1.75  
 (3a)^2-2a^2=1.75.......7a^2=1.75.....a^2=0.25.......a=0.5 , as a>0

A

PayelRB · Answer

Hi,

This is a great explanation, but how are you arriving at product of the roots = a^2 ?

Crytiocanalyst · Answer

let the roots of the equation be w and b 
then 
(w+b)^2 -2wb = 1.75

Sum of the roots = 3a
product of the roots = a^2

9a^2 -2a^2 = 1.75
=>7a^2=1.75
=>a^2=2.5 and a>0

therefore a=0.5 
Hence IMO A

If the square of the roots of the equation x^2 - 3ax + a^2 = 0, find a

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If the square of the roots of the equation x^2 - 3ax + a^2 = 0, find a

Prep Toolkit

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