if $16x^4-24x^3+41x^2-kx+16$ is a perfect square of polynomial function, then value of $k$ is
i have equate expression by $(ax^2+bx+c)^2$
but after expanding it and equation coeff. both side is hard wark
could some help me with this, thanks
if polynomial expression is a perfect square, then finding $k$
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algebra-precalculus
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1You can find $a^2$ and $c^2$, right? – 2017-01-02
1 Answers
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Expanding $(ax^2+bx+c)^2 = a^2x^4 + 2abx^3 + (2ac+b^2) x^2 + 2bcx+c^2,$ you can get $a=\pm 4, c=\pm 4.$ We let $a=4$ and determine $b,c:$
$2ab=-24,$ so $b=-3.$
$2ac+b^2 = 41,$ so $c=4.$
Hence the answer is $k=-2bc=24.$