Question

please solve question no. 21

please solve ​

Answer 1

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Step by step solution:

$Given \ p(x)=x^4+ax^3-7x^2-8x+b \ and \ two \ factors \ (x+2) \ and \ (x+3)\\\\putting \ value \ of \ x \ to \ get \ value \ of \ a \ and \ b\\\\g(x)=x+2=0\\\\x=-2\\\\f(x)=x+3=0\\\\x=-3\\\\putting \ these \ value \ in \ p(x)$

$p(x)=x^4+ax^3-7x^2-8x+b\\\\p(-2)=16-8a-28+16+b=0\\\\b=8a-4 \ .....(i)\\\\Now \ putting \ x=-3\\\\p(x)=x^4+ax^3-7x^2-8x+b\\\\p(-3)=81-27a-63+24+b=0\\\\42-27a+b=0\\\\b=27a-42 \ ....(ii)\\\\From \ equation \ (i) \ and \ (ii)\\\\8a-4=27a-42\\\\19a=38\\\\a=2\\\\putting \ a=2 \ in \ (i)\\\\b=8a-4\\\\b=16-4\\\\b=12\\\\So \ we \ get \ a=2 \ and \ b=12$

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Answer 2

Answer:

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