Answer:
The zeros are:
[tex]x=-1,\:x=\frac{3}{2}[/tex]
Step-by-step explanation:
As the function is given by
[tex]F(x)=4x^4-4x^3-11x^2+6x+9[/tex]
We have to find the zeros of [tex]4x^4-4x^3-11x^2+6x+9[/tex].
So,
[tex]4x^4-4x^3-11x^2+6x+9=0[/tex]
Factor left side of equation.
[tex]\left(x+1\right)^2\left(2x-3\right)^2=0[/tex]
[tex]\mathrm{Using\:the\:Zero\:Factor\:Principle:\quad \:If}\:ab=0\:\mathrm{then}\:a=0\:\mathrm{or}\:b=0\:\left(\mathrm{or\:both}\:a=0\:\mathrm{and}\:b=0\right)[/tex]
[tex]Solving\:x+1=0[/tex]
[tex]\mathrm{Subtract\:}1\mathrm{\:from\:both\:sides}[/tex]
[tex]x+1-1=0-1[/tex]
[tex]x=-1[/tex]
[tex]Solving\:2x-3=0[/tex]
[tex]x=\frac{3}{2}[/tex]
So, the zeros are:
[tex]x=-1,\:x=\frac{3}{2}[/tex]
Keywords: zeros, equation
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