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Question

If α,β are the roots of the equation ax2+bx+c=0 such that β<α<0, then the quadratic equation whose roots are |α|,|β| is given by



A

|α|x2+|b|x+|c|=0

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B

ax2|b|x+c=0

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C

|a|x2|b|x+|c|=0

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D

a|x|2+b|x|+c=0

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Solution

The correct option is C

|a|x2|b|x+|c|=0


Sum of roots=|α|+|β|=αβ  (α<0 and β<0)=(α+β)=(ba)=ba=ba(|α|+|β|>0)
and product of roots =|α||β|=|αβ|=ca
Hence, required equation is
x2(ba)x+ca=0or |a|x2|b|x+|c|=0.


Mathematics

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