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

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Answer 1 · 2016-12-08T13:11:20

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

$2 x^{2} - 3 x + 4 = 0$ $2x^2-3x+4=0$

let $α, β$ $" "alpha,beta" "$ be the roots

$α + β = - \frac{- 3}{2} = \frac{3}{2}$ $alpha+beta=-(-3)/2=3/2$

$α β = \frac{4}{2} = 2$ $alphabeta=4/2=2$

eqn with roots $α + 2, β + 2$ $" "alpha+2," "beta+2$

let $A = α + 2; B = β + 2$ $" "A=alpha+2; B=beta+2$

$A + B = α + 2 + β + 2 = α + β + 4 = \frac{3}{2} + 4 = \frac{11}{2}$ $A+B=alpha+2+beta+2=alpha+beta+4=3/2+4=11/2$

$A B = (α + 2) (β + 2) = α β + 2 α + 2 β = 4$ $AB=(alpha+2)(beta+2)=alphabeta+2alpha+2beta=4$

$A B = α β + 2 (α + β) + 4 = 2 + 2 \times \frac{3}{2} + 4 = 9$ $AB=alphabeta+2(alpha+beta)+4=2+2xx3/2+4=9$

new eqn.

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

$X^{2} - \frac{11}{2} X + 9 = 0$ $X^2-11/2X+9=0$

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

If a and B are the roots of the equation 2x2−3x+4=02x^2 - 3x + 4 = 0, how do you form the equation with roots a+2 and B+2?