The equation whose roots are $1, 1,-2$ is
- $x^{3}+3x-2=0$
- $x^{3}+x-2=0$
- $x^{3}+2x-3=0$
- $x^{3}-3x+2=0$
Reveal answer
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Correct answer
Explanation
If roots are 1, 1, -2, the polynomial is (x - 1)(x - 1)(x + 2) = (x^2 - 2x + 1)(x + 2) = x^3 + 2x^2 - 2x^2 - 4x + x + 2 = x^3 - 3x + 2 = 0.
AI explanation
A cubic equation with roots 1, 1, and -2 is constructed using the relationship between roots and coefficients. The sum of the roots is 1 + 1 - 2 = 0, which equals the negated coefficient of x^2. The sum of the product of roots taken two at a time is (1*1) + (1*-2) + (1*-2) = -3, which equals the coefficient of x. The product of the roots is 1 * 1 * -2 = -2, which equals the negated constant term. The resulting equation is x^3 - 3x + 2 = 0.