Question

What are the roots of the polynomial equation x cubed minus 5 x + 5 = 2 x squared minus 5?

Answer 1

Roots of the polynomial $x^3-5x+5=2x^2-5$ are $x=\sqrt{5},x=-\sqrt{5}\,\,and\,\,x=2$

Step-by-step explanation:

We need to find roots of the polynomial equation: $x^3-5x+5=2x^2-5$

Solving the polynomial to find roots:

$x^3-5x+5=2x^2-5\\Rearranging:\\x^3-5x+5-2x^2+5=0\\x^3-2x^2-5x+10=0$

Finding factors by grouping:

$(x^3-2x^2)(-5x+10)=0\\Finding\,\,common\,\,terms:\\x^2(x-2)-5(x-2)=0\\(x^2-5)(x-2)=0\\x^2-5=0\,\,and\,\,x-2=0\\x^2=5\,\,and\,\,x=2\\x=\pm \sqrt{5}\,\,and\,\,x=2$

So, roots of the polynomial $x^3-5x+5=2x^2-5$ are $x=\sqrt{5},x=-\sqrt{5}\,\,and\,\,x=2$

Keywords: Roots of Polynomial

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