Is Cubic Equation Formula Needed?

Algebra Level 2

Enter the sum of absolute values of the integer solutions to the following equation.

x 3 + 3 x 2 − 4 x = 12 x^3+3x^2-4x=12


The answer is 7.

Muhammad Rasel Parvej by Muhammad Rasel Parvej , 27, Bangladesh

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1 solution

x 3 + 3 x 2 − 4 x = 12 x^3+3x^2-4x=12 ⟹ x 2 ( x + 3 ) − 4 ( x + 3 ) = 0 \implies x^2(x+3)-4(x+3)=0 ⟹ ( x + 3 ) ( x 2 − 4 ) = 0 \implies (x+3)(x^2-4)=0 ⟹ x = − 3 , 2 , − 2 \implies x=-3, 2, -2

So, the answer is ∣ − 3 ∣ + ∣ 2 ∣ + ∣ − 2 ∣ = 7 |-3|+|2|+|-2|=\boxed{7} .

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Nice! I stumbled upon x=2 and then used synthetic division.

Jerry McKenzie - 3 years, 5 months ago

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