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if alpha + beta are the zeros of polynomial f(x)= x^2 - 2 x + 5 then find the quadratic polynomial whose zeros are alpha + beta and 1/alpha + 1/beta

Posted by Ayushi Uniyal 6 years, 2 months ago

CBSE > Class 10 > Mathematics

1 answers

Prachi Janwani 6 years, 2 months ago

f(x)= x^2-2x+5 Alpha and beta are the zeros of f(x) alpha+beta = -b/a= -(-2)/1= 2 alpha×beta = c/a= 5/1= 5 Now, new zeros are alpha+beta and 1/alpha+1/beta Sum of new zeros= alpha + beta+1/alpha +1/beta = 2 + (alpha+beta)/apha×beta = 2 + 2/5 = (10+2)/5 = 12/5 Product of new zeros = alpha+beta×1/alpha+1/beta = 2×(alpha+beta)/alpha×beta = 2×2/5 = 4/5 Quadratic polynomial= K[x^2-(sum of zeros)x+ product of zeros] = K[x^2-(12/5)x+4/5] = K[(5x^2-12x+4)/5] K is a constant Therefore, k=5 = 5[(5x^2-12x+4)/5] = 5x^2-12x+4

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CBSE > Class 10 > Mathematics