Roots of the polynomial [tex]x^3-5x+5=2x^2-5[/tex] are [tex]x=\sqrt{5},x=-\sqrt{5}\,\,and\,\,x=2[/tex]
Step-by-step explanation:
We need to find roots of the polynomial equation: [tex]x^3-5x+5=2x^2-5[/tex]
Solving the polynomial to find roots:
[tex]x^3-5x+5=2x^2-5\\Rearranging:\\x^3-5x+5-2x^2+5=0\\x^3-2x^2-5x+10=0[/tex]
Finding factors by grouping:
[tex](x^3-2x^2)(-5x+10)=0\\Finding\,\,common\,\,terms:\\x^2(x-2)-5(x-2)=0\\(x^2-5)(x-2)=0\\x^2-5=0\,\,and\,\,x-2=0\\x^2=5\,\,and\,\,x=2\\x=\pm \sqrt{5}\,\,and\,\,x=2[/tex]
So, roots of the polynomial [tex]x^3-5x+5=2x^2-5[/tex] are [tex]x=\sqrt{5},x=-\sqrt{5}\,\,and\,\,x=2[/tex]
Keywords: Roots of Polynomial
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