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Question

If α, β are roots of the equation x2+lx+m=0, write an equation whose roots are -1αand-1β.

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Solution

Given equation: x2 + lx + m = 0
Also, α and β are the roots of the equation.
Sum of the roots = α + β = -l1 = -l

Product of the roots = αβ = m1 = m
Now, sum of the roots = -1α - 1β =-α + βαβ =- -lm = lm
Product of the roots = 1αβ = 1m

x2-Sum of the rootsx+Product of the roots=0x2 - lmx + 1m = 0 mx2 - lx + 1= 0

Hence, this is the equation whose roots are -1α and -1β.

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