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Let be the roots of the quadratic equation
MATHEMATICS · Single correct · CBSE · Mathematics · Polynomials · Polynomials
Problem Let α , β \alpha, \beta α , β be the roots of the quadratic equation a x 2 + b x + c = 0 ax^2 + bx + c = 0 a x 2 + b x + c = 0 , then the roots of the equation a ( x + 1 ) 2 + b ( x + 1 ) ( x − 2 ) + c ( x − 2 ) 2 = 0 a(x+1)^2 + b(x+1)(x-2) + c(x-2)^2 = 0 a ( x + 1 ) 2 + b ( x + 1 ) ( x − 2 ) + c ( x − 2 ) 2 = 0 are :
(a) 2 α + 1 α − 1 , 2 β + 1 β − 1 \frac{2\alpha+1}{\alpha-1}, \frac{2\beta+1}{\beta-1} α − 1 2 α + 1 , β − 1 2 β + 1
(b) 2 α − 1 α + 1 , 2 β − 1 β + 1 \frac{2\alpha-1}{\alpha+1}, \frac{2\beta-1}{\beta+1} α + 1 2 α − 1 , β + 1 2 β − 1
(c) α + 1 α − 2 , β + 1 β − 2 \frac{\alpha+1}{\alpha-2}, \frac{\beta+1}{\beta-2} α − 2 α + 1 , β − 2 β + 1
(d) 2 α + 3 α − 1 , 2 β + 3 β − 1 \frac{2\alpha+3}{\alpha-1}, \frac{2\beta+3}{\beta-1} α − 1 2 α + 3 , β − 1 2 β + 3
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