If alpha and beta are the zeroes of the quadratic polynomial f(x) =x2-2x+1,then find a quadratic polynomial whose zeroes are2alpha/beta and2beta/alpha

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Solution

Dear Student,

$F (x) = x^{2} - 2 x + 1 r o o t o f f (x) x^{2} - 2 x + 1 = 0 {(x - 1)}^{2} = 0 x = 1, 1 α = 1 a n d β = 1 t h e n 2 \frac{α}{β} = 2 a n d 2 \frac{β}{α} = 2 n o w q u a d r a t i c p o l y n o m i a l i s x^{2} - (s u m o f r o o t s) x + (p r o d u c t o f r o o t s) = 0 x^{2} - (2 + 2) x + 2 \times 2 = 0 x^{2} - 4 x + 4 = 0$

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and

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are the zeros of the quadratic polynomial

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and

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If alpha and beta are the zeroes of the quadratic polynomial f(x) =x2-2x+1,then find a quadratic polynomial whose zeroes are2alpha/beta and2beta/alpha

Dear Student, F(x) = x2-2x+1root of f(x)x2-2x+1=0(x-1)2 = 0x =1,1α=1 and β=1then 2αβ= 2 and 2βα = 2now quadratic polynomial is x2-(sum of roots)x+ (product of roots) = 0x2-(2+2)x + 2×2 =0x2-4x+4 = 0 Regards