Relation between Roots and Coefficients for Quadratic
Let α, β be t...
Question
Let α,β be the roots of the quadratic equation 3x2+10x+2=0, then the quadratic equation whose roots are αα+5,ββ+5, is
A
46x2+27x+2=0
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B
27x2+2x+48=0
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C
27x2+48x+2=0
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D
27x2+46x+2=0
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Solution
The correct option is D27x2+46x+2=0 Let y=xx+5, where x=α,β xy+5y=x⇒x=5y1−y Putting x=5y1−y in the quadratic equation 3x2+10x+2=0⇒3(5y1−y)2+10(5y1−y)+2=0⇒75y2+50y(1−y)+2(1−y)2=0⇒27y2+46y+2=0
Hence, the quadratic equation whose roots are αα+5,ββ+5 is 27x2+46x+2=0