Question
Download Solution PDFIf ax2 + bx + c = 0 and bx2 + cx + a = 0 have a common root a ≠ 0 then
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
1. Condition for one and two common roots:
If both roots are common, then the condition is
2. a3 + b3 + c3 - 3abc = (a + b + c)(a2 + b2 + c2 - ab - bc - ca)
If a = b = c, then
a3 + b3 + c3 = 3abc
Calculation:
Given that,
ax2 + bx + c = 0 ----(1)
bx2 + cx + a = 0 ----(2)
According to the question, both roots of equations (1) and (2) are common. Therefore, using the concept discussed above
This will be possible only if
⇒ a = b, b = c, c = a
⇒ a3 + b3 + c3 = 3abc
⇒
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