find-real-q-so-that-x-4-40x-2-q-0-has-four-real-solution-forming-AP-

Question Number 93705 by i jagooll last updated on 14/May/20

find real q so that x^{4} - {40 x}^{2} + q = 0

has four real solution forming

AP .

Commented by PRITHWISH SEN 2 last updated on 14/May/20

let the roots are a - 3 b, a - b, a + b, a + 3 b

∴ the sum of the roots

4 a = 0 \Rightarrow a = 0

and the product of two roots at a time

- 10 b^{2} = 40 \Rightarrow b = \pm 2

the roots are - 6, - 2, 2, 6

∴ q = 36 \times 4 = 144 . please check .

Commented by i jagooll last updated on 14/May/20

correct sir. but my way is different

Commented by PRITHWISH SEN 2 last updated on 14/May/20

then post it . I have also lots to learn .