If a and B are the roots of the equation #2x^2 - 3x + 4 = 0#, how do you form the equation with roots a+2 and B+2?

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Answer 1 · 2016-12-08T13:11:20

#2X^2-11X+18=0#

#2x^2-3x+4=0#

let#" "alpha,beta" "# be the roots

#alpha+beta=-(-3)/2=3/2#

#alphabeta=4/2=2#

eqn with roots #" "alpha+2," "beta+2#

let#" "A=alpha+2; B=beta+2#

#A+B=alpha+2+beta+2=alpha+beta+4=3/2+4=11/2#

#AB=(alpha+2)(beta+2)=alphabeta+2alpha+2beta=4#

#AB=alphabeta+2(alpha+beta)+4=2+2xx3/2+4=9#

new eqn.

#X^2-(A+B)X+AB=0#

#X^2-11/2X+9=0#

#2X^2-11X+18=0#