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anonymous
 one year ago
What is the sum of the roots of the equation listed below?
anonymous
 one year ago
What is the sum of the roots of the equation listed below?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[(x\sqrt2)(x^2\sqrt3x+\pi)=0\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0for a quadratic \(ax^2+bx+c\) the sum of the roots is \(b/a\); observe: $$a(xr_1)(xr_2)=a(x^2(r_1+r_2)x+r_1r_2)=ax^2\underbrace{a(r_1+r_2)}_bx+\underbrace{ar_1r_2}_c\\\implies b =a(r_1+r_2)\\\implies r_1+r_2=\frac{b}a$$

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the sum of the roots of \(x^2\sqrt3x+\pi\) is \((\sqrt3)/1=\sqrt3\), and then the root of \(x\sqrt2\) is clearly \(\sqrt2\) so the total sum of our roots is \(\sqrt2+\sqrt3\). this is because the roots of a product of two polynomials is simply the combined roots of both individual polynomials

Directrix
 one year ago
Best ResponseYou've already chosen the best response.0Sum of the Roots of a Polynomial Theorem Attached

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this chart is really helpful, thanks
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