Question

Given: |abaα+bbcbα+cac+bbc+c0|=0 Applying C3→C3−(αC1+C2)If the determinant |ab0bc0aα+bbc+c−(ac2+2bc+c)|=0⇒−(aα2+2bα+c)(ac−b2)=0⇒aα2+2bα+c=0 or b2=ac∴α is root of ax2+2bx+c or a,b,c are in GP.

• A. (A) a, b, c are in AP
• B. (B) a, b, c are in GP
• C. (C) a, b, c are in HP
• D. (D) (x -α ) is a factor of ax2 + 2bx + c

Answer 1

Answer: (A), (D)

(A) a, b, c are in AP

Answer 2

Explanation:
|abac+bbcbc+cac+bbc+c0| is equal to zero, then