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.

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

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

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

If a and B are the roots of the equation 2x^2 - 3x + 4 = 02x^2 - 3x + 4 = 0, how do you form the equation with roots a+2 and B+2?