Question
Mathematics Question on Quadratic Equations
If p + q + r = a + b + c = 0, then the determinant Δ=|paqbrcqcrapbrbpcqa| equals
A
(A) 0
B
(B) 1
C
(C) pa + qb + rc
D
(D) None of these
Answer
(A) 0
Explanation
Solution
Explanation:
We have Δ=pqr(a3+b3+c3)−abc(p3+q3+r3)But a+b+c=0⇒(a+b)3=−c3⇒a3+b3+3ab(a+b)+c3=0⇒a3+b3+c3=−3ab(−c)=3abcSimilarly, p3+q3+r3=3pqrThus, Δ=pqr(3abc)−abc(3pqr)=0