If x²-3x+2 is a factor of 2x⁴+ ax³ +3x²+3x-2, then find the value of 'a'.

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asked Mar 20, 2024 52.3k views

4 votes

If x²-3x+2 is a factor of 2x⁴+ ax³ +3x²+3x-2, then find the value of 'a'.

Mathematics
college

Sebastian Weber asked

by Sebastian Weber

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1 Answer

6 votes

Answer:

HI,

a=-6

Explanation:

$\\x^2-3x+2=x^2-2x-x+2=x(x-2)-(x-2)=(x-2)(x-1)\\roots\ are\ 2\ and\ 1.\\\\P(x)=2x^4+ax^3+3x^2+3x-2\\\\P(2)=0=2*2^4+8a+12+6-2=8a+48\\8a=-48\\\\a=-6\\\\P(1)=0=2*1^4+a*1^3+3*1^2+3*1-2=2+a+3+3-2=a+6\\a=-6\\$

Farski answered Mar 25, 2024

by Farski

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