Question
Download Solution PDFIf k is one of the roots of the equation x(x + 1) + 1 = 0, then what is its other root?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
For a quadratic equation ax2 + bx + c = 0
The sum of the roots =
The product of the roots =
Calculation:
Let the other root be β
Given equation is x(x + 1) + 1 = 0
⇒ x2 + x + 1 = 0
a = 1, b = 1 and c = 1
As k is the root of the equation
⇒ k2 + k + 1 = 0
⇒ k2 = -1 - k .....(i)
The sum of the roots =
⇒ β + k = -1
⇒ β = -1 - k .....(ii)
From equation (i) and (ii), we get
⇒ β = k2
∴ The other root = k2
Given equation is x(x + 1) + 1 = 0
Factor of (x2 + x + 1) = 0
⇒ x = ω or ω2
Consider k = ω
∴ The other root = ω2 = k2
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