Transformation of Roots: Linear Combination of Roots
If α, β are t...
Question
If α,β are the roots of 3x2−2x+1=0, then the equation whose roots are −α3,−β3 is
A
27x2+6x−1=0
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B
27x2−6x+1=0
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C
27x2+6x+1=0
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D
9x2+6x+1=0
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Solution
The correct option is C27x2+6x+1=0 f(x)=3x2−2x+1 f(x)=0→α,β are the roots.
The equation whose roots are −α3,−β3 is f(−3x)=0 ⇒3(−3x)2−2(−3x)+1=0⇒27x2+6x+1=0