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Question

# If α & β are the roots of the equation ax2+bx+c=0, The equation whose roots are 1+1α,1+1β will be:

A
cx2+(b+2c)x+(a+b+c)=0
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B
ax2+(a+b2c)x+2(ab+c)=0
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C
cx2+2(bc)x+(ab+c)=0
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D
cx2+(b2c)x+(ab+c)=0
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Solution

## The correct option is D cx2+(b−2c)x+(a−b+c)=0Given: α,β are the roots of the equation ax2+bx+c=0 To find: Equation with roots 1+1α,1+1β Let y=1+1x ⇒x=1y−1 Substituting x=1y−1 in ax2+bx+c=0, we get: a(1y−1)2+b(1y−1)+c=0 ⇒a+b(y−1)+c(y−1)2=0 ⇒a+by−b+cy2−2cy+c=0 ⇒cy2+(b−2c)y+(a−b+c)=0 Now, In terms of x, we get the equation as: cx2+(b−2c)x+(a−b+c)=0 which is required equation.

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