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Question

Find the quadratic equation whose roots are the additive inverses of the roots of the equation x25x+6=0.

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Solution

First we have to find the roots of the equation x25x+6=0
x25x+6
x22x3x+6=x(x2)3(x2)(x2)(x3)=0(x2)=0 or (x3)=0x=2,3
Now the roots of the required equation are the additive inverses of 2,3. i.e. -2,-3. So the required equation is
(x(2))(x(3))=0(x+2)(x+3)=0x2+5x+6=0
Therefore the required equation is x2+5x+6=0.

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