Transformation of Roots: Linear Combination of Roots
If α, β are t...
Question
If α,β are the roots of 2x2+5x+1=0, then the equation whose roots are 2α+1,2β+1 is
A
x2−3x−2=0
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B
x2+3x−2=0
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C
x2+3x+2=0
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D
x2−3x+2=0
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Solution
The correct option is Bx2+3x−2=0 f(x)=2x2+5x+1=0→α,β are the roots.
Let y=2x+1, where x=α,β x=y−12
The equation whose roots are 2α+1,2β+1 is, f(x−12)=0 ⇒2(x−1)24+5(x−1)2+1=0 ⇒(x−1)2+5(x−1)+2=0⇒x2+3x−2=0