Question

The roots a, ß of the equation x^2 – 3ax + a2 = 0 are such that alpha^2 + ß^2 = 1.75. Find the value of a.
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Answer 1

Answer:

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Step-by-step explanation:

given an equation x^2-3ax+a^2=0...(1)

and

squares of its roots

alpha^2+beta^2=1.75...(2)

from eq(1)

sum of roots is alpha+beta=3a

product of roots=alpha*beta=a^2

from (2)

(alpha+beta)^2-2*alpha*beta=(3a)^2-2*a^2=9a^2-2a^2=7a^2

7a^2=1.75(given)

a^2=0.25

a=0.5