If the equation 2x^3 + 5x^2 - 4x - 12 = 0 has | vedclass

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(A) Given equation: $2x^3 + 5x^2 - 4x - 12 = 0$ Factorizing the cubic equation: $2x^3 + 4x^2 + x^2 + 2x - 6x - 12 = 0$ $2x^2(x + 2) + x(x + 2) - 6(x +

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$-6$

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(A) Given equation: $2x^3 + 5x^2 - 4x - 12 = 0$ Factorizing the cubic equation: $2x^3 + 4x^2 + x^2 + 2x - 6x - 12 = 0$ $2x^2(x + 2) + x(x + 2) - 6(x + 2) = 0$ $(2x^2 + x - 6)(x + 2) = 0$ $(2x - 3)(x + 2)(x + 2) = 0$ The roots are $x = -2, -2, \frac{3}{2}$. The distinct roots are $-2$ and $\frac{3}{2}$. The quadratic equation with these roots is: $(x - (-2))(x - \frac{3}{2}) = 0$ $(x + 2)(x - \frac{3}{2}) = 0$ $x^2 - \frac{3}{2}x + 2x - 3 = 0$ $x^2 + \frac{1}{2}x - 3 = 0$ Multiplying by $2$ to clear the fraction: $2x^2 + x - 6 = 0$ The constant term is $-6$.

If the equation $2x^3 + 5x^2 - 4x - 12 = 0$ has a repeated root,then the constant term of the quadratic equation whose roots are the distinct roots of the given equation is

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