Question

If `a ,b ,c(a b c^2)x^2+3a^2c x+b^2c x-6a^2-a b+2b^2=0` ares rational.
A. rational
B. imaginary
C. irratiional
D. none of these

Answer 1

Correct Answer - A
Let D both discriminant of the given equation. Then,
`D = (3a^(2)+b^(2))^(2) c^(2) + 4 abc^(2)+4abc^(2)(6a^(2) + ab - 2b^(2))`
`rArr" "D = c^(2)[9 a^(4)+b^(4)+6a^(2)b^(2)+24a^(3)b + 4a^(2)b^(2) - 8 ab^(3)]`
`rArr" "D = c^(2)[9a^(4) + b^(4) + 16a^(2)b^(2) - 6a^(2)b^(2)+24a^(3) b - 8 ab^(3)]`
`rArr" "D = c^(2) (3a^(2)-b^(2) + 4ab)^(2)`
Clearly, discriminant is a perfect square. So, roots are rational.