Maths · Relations between roots and coefficients, nature of roots
If the sum of the roots of the equation is equal to sum of the squares of their
If the sum of the roots of the equation \( a x^{2}+b x+c=0 \) is equal to sum of the squares of their reciprocals, then \( b c^{2}, c a^{2}, a b^{2} \) are in
- A. \( A . P \)
- B. \( G . P \)
- C. \( H . P \)
- D. A.G.P
Step-by-step solution
Let α, β be roots. Given α+β = 1/α² + 1/β². Using sum S = -b/a, product P = c/a, we derive -b/a = (S² - 2P)/P². Substituting and simplifying gives a b² + b c² = 2 a² c. Denote X = bc², Y = ca², Z = ab². Then Z + X = 2Y, so X, Y, Z are in A.P.