claudia4swim
Answered

Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Experience the ease of finding reliable answers to your questions from a vast community of knowledgeable experts. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.

Find all zeros of the function and write the polynomial as a product of linear factors
f(x)=x^4+29x^2+100

Sagot :

take x² = t 
t²+29t+100
=(t²+25t) +(4t+100)
=t(t+25) + 4(t+25)
=(t+4)(t+25)
=(x²+4)(x²+25)
[tex]f(x)=x^4+29x^2+100=\left(x^2\right)^2+29x^2+100\\\\x^2=v;\ v\geq0\\\\f(v)=v^2+29v+100\\\\a=1;\ b=29;\ c=100\\\\\Delta=b^2-4ac;\ v_1=\frac{-b-\sqrt\Delta}{2a};\ v_2=\frac{-b+\sqrt\Delta}{2a}\\\\\Delta=29^2-4\cdot1\cdot100=841-400=441;\ \sqrt\Delta=\sqrt{441}=21\\\\v_1=\frac{-29-21}{2\cdot1}=\frac{-40}{2}=-20 < 0;\ v_2=\frac{-29+21}{2\cdot1}=\frac{-8}{2}=-4 < 0[/tex]

[tex]Function\ has\ no\ zeros.\\\\\\f(x)=x^4+29x^2+100=x^4+25x^2+4x^2+100\\\\=x^2(x^2+25)+4(x^2+25)=(x^2+25)(x^2+4)\\\\is\ not\ impossible\ write\ the\ polynomia\l as\ a\ product\ of\ linear\ factors.[/tex]
Thank you for your visit. We are dedicated to helping you find the information you need, whenever you need it. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting Westonci.ca. Stay informed by coming back for more detailed answers.