The equation whose roots are $-2,1,3$, is
- $x^{3}+2x^{2}+3x-6=0$
- $x^{3}-2x^{2}-5x+6=0$
- $x^{3}+x^{2}-x-1=0$
- $x^{3}-x^{2}+x+1=0$
Reveal answer
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B
Correct answer
Explanation
The polynomial with roots -2, 1, 3 is (x+2)(x-1)(x-3) = (x^2+x-2)(x-3) = x^3 - 3x^2 + x^2 - 3x - 2x + 6 = x^3 - 2x^2 - 5x + 6.
AI explanation
The required cubic equation is formed by setting the product of (x-r) for each root r to zero. The required equation is (x+2)(x-1)(x-3)=0. First, multiply (x+2) and (x-1) to get x^2+x-2. Multiplying this result by (x-3) gives x^3 - 3x^2 + x^2 - 3x - 2x + 6 = 0. Combining like terms results in the equation x^3 - 2x^2 - 5x + 6 = 0.