Let a,b,c and d be distinct real numbers. Show that the equation (x-b)(x-c)(x-d)+(x-a)(x-c)(x-d)+

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Show that roots of (x-a)(x-c) + 2(x-b)(x-d) are real and distinct. Show that roots of (x-a)(x-c) + 2(x-b)(x-d) are real and distinct.
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Let α, β, γ be the roots of (x-a)(x-b)(x-c)=d, d≠0 then the roots of the equation (x-α)(x-β)(x-γ) + Let α, β, γ be the roots of (x-a)(x-b)(x-c)=d, d≠0 then the roots of the equation (x-α)(x-β)(x-γ) +