Question

\[\alpha\] is a root of
\[4x^{2}+2x-1=0\] and \[f(x)=4x^{3}-3x+1\]then \[2(f(\alpha)+\alpha)=?\]

Answer 1

\( 4a^2+2a-1=0 \) so u have \( 4a^2=-2a+1 \)

then

\( 2(f(a)+a)=2f(a)+2a=8a^3-6a+2+2a=8a^3-4a+2=2a(-2a+1)-4a+2 \)

Answer 2

check it

Answer 3

that is f(alpha)

Answer 4

yes i mean alpha by a

Answer 5

ok

Answer 6

then

Answer 7

well then \(2a(-2a+1)-4a+2=-4a^2-2a+2=-(4a^2+2a-1)+1=0+1=1 \)

Answer 8

let me know if u have any doubt

Answer 9

explain after this 8a3−4a+2

Answer 10

ok
8a^3=4a^2 (2a) and i replaced 4a^2 with -2a+1 because quadratic equation gives us 4a^2=-2a+1

Answer 11

what about +2 in 8a3−4a+2

Answer 12

2f(a)=2(4a^3-3a+1)=8a^3-6a+2
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Answer 13

where is +2 here 8a^3=4a^2 (2a)

Answer 14

sorry which +2