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Opalg · #5 January 5th, 2009, 01:21 PM

Quote:

Originally Posted by mathaddict

Given that (x-3) and (2x+1) are factors of
$f(x)=ax^4+bx^3+13x^2=30x+9$ , find the values of a and b . With these values of a and b , show that $f(x)\geq0$ for all x belongs to real numbers .

My working :

i found that a = 4 and b = -20

$4x^4-20x^3+13x^2+30x+9$
$(x-3)(2x+1)(2x^2-5x-3)$

I am wondering how can i show that $f(x)\geq0$ from here .
Thanks for any help .

Try factorising $2x^2-5x-3$ .

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