Question

If a, b, c are in G.P. then the equation ax² + 2bx + c = 0 and dx² + 2ex + f = 0 have a common root if d/a , e/b, f/c are in :

• A. AP
• B. GP
• C. HP
• D. None of these

Answer 1

Answer: (A)

AP

Answer 2

Here b = $\sqrt{ac}$ (As a, b, c ® GP)

So, ax² + 2$\sqrt{ac}$ + c = 0 Ž (x$\sqrt{a}$+$\sqrt{c}$)² = 0

or x = –$\sqrt{c}$/$\sqrt{a}$, Now, substituting in eqⁿ (2);

dc/a – 2e$\sqrt{c}$/$\sqrt{a}$ + f = 0 Ž d/a – 2e/$\sqrt{ac}$ + f/c = 0

Ž d/a –2e/b + f/c = 0