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If α and β are the zeros of the quadratic polynomial f(x)=2x^2-5x+7. Find a polynomial whose zeros are 2α+3β and 3α+2β.

Posted by Mayank Parauha 7 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Misha Jain 7 years, 7 months ago

Alpha + beta = 5/2 Alpha× beta = 7/2 For new polynomial we have zeroes 2alpha + 3 beta and 3alpha+2beta S= sum of zeroes = 2alpha+3beta+3alpha+2beta = 5alpha + 5beta = 5 ( alpha + beta ) = 5 (5/2) = 25/2 P = product of zeroes = (2alpha+3beta)(3alpha+2beta) = 6alpha ^2 + 4 alpha× beta +9 alpha × beta +6 beta^2 = 6 (alpha^2+beta^2) + 13 alpha × beta = 6 (( alpha +beta)^2 -2 alpha×beta ) +13 alpha × beta = 6 ( alpha+ beta )^2 -12 alpha×beta+13alpha×beta =6 ( alpha+ beta )^2 + alpha ×beta = 6(5/2)^2 +7/2 =6 (25/4) +7/2 = 75/2 +7/2 =82/2=41 Required quadtratic polynomial us given by x^2-sx+px = x^2 -(25/2)x +41 =2x^2+25x+82

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