An interesting equation

Algebra Level 5

The equation x 3 + 12 x 2 − x − 7 = 0 x^3+12x^2-x-7=0 has three real roots. Now, the equation a y 3 + b y 2 − c y + d = 0 ay^3+by^2-cy+d=0 has the roots of the previous equation increased by 4 4 , where gcd ( a , b , c , d ) = 1 \text{gcd}(a,b,c,d)=1 . Find a + b + c + d a+b+c+d


The answer is 175.

Alan Enrique Ontiveros Salazar by Alan Enrique Ontiveros S… , 22

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1 solution

Nikky Fauzdar
Mar 1, 2014

let a be the root of eq x^3+12x^2-x-7=0 and roots of another eq increase root of this eq by 4 so y=x+4 and x=y-4 put this value of x and we get y^3-49y+125=0 and on comparing value of a=1 b=0 c=49 d=125 hence a+b+c+d=175

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