Question
Download Solution PDFIf the roots of the equation x2 - ax - bx - cx + bc + ca = 0 are equal, then which one of the following is correct?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
For a quadratic equation ax2 + bx + c = 0,
Discriminant (D) = b2 - 4ac
For equal roots, D = 0
Formula used:
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Calculation:
Given that,
x2 - ax - bx - cx + bc + ca = 0
⇒ x2 - (a + b + c)x + bc + ca = 0
For equal roots, D = 0
⇒ [-(a + b + c)]2 - 4(bc + ca) = 0
⇒ a2 + b2 + c2 + 2ab + 2bc + 2ca - 4bc - 4ca = 0
⇒ a2 + b2 + c2 + 2ab - 2bc - 2ca = 0
Using the above formula, we can write
(a + b - c)2 = 0
∴ a + b - c = 0
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