Transformation of Roots: Linear Combination of Roots
If α, β are t...
Question
If α,β are the roots of the equation x2−(3+√25log24−log2(log3(log6216))x−2(3log32−2log23)=0, then the equation whose roots are −α,−β is
A
x2+19x+2=0
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B
x2+35x−2=0
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C
x2+29x+2=0
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D
x2+35x+2=0
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Solution
The correct option is Dx2+35x+2=0 x2−(3+√25log24−log2(log3(log6216))x−2(3log32−2log23)=0 ⇒x2−(3+√2log245−log2(log33))x+2=0 ⇒x2−(3+√210)x+2=0 ⇒x2−(3+25)x+2=0 ⇒x2−35x+2=0