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(B) Given the equation $x^2 - 2cx + ab = 0$ has real and unequal roots,its discriminant $D_1 > 0$. $D_1 = (-2c)^2 - 4(1)(ab) = 4c^2 - 4ab > 0$,which i

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imaginary

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(B) Given the equation $x^2 - 2cx + ab = 0$ has real and unequal roots,its discriminant $D_1 > 0$. $D_1 = (-2c)^2 - 4(1)(ab) = 4c^2 - 4ab > 0$,which implies $c^2 > ab$. Now,consider the equation $x^2 - 2(a + b)x + a^2 + b^2 + 2c^2 = 0$. The discriminant $D_2$ of this equation is: $D_2 = [-2(a + b)]^2 - 4(1)(a^2 + b^2 + 2c^2)$ $D_2 = 4(a^2 + 2ab + b^2) - 4a^2 - 4b^2 - 8c^2$ $D_2 = 4a^2 + 8ab + 4b^2 - 4a^2 - 4b^2 - 8c^2$ $D_2 = 8ab - 8c^2 = 8(ab - c^2)$. Since $c^2 > ab$,it follows that $ab - c^2 Therefore,$D_2 Since the discriminant is negative,the roots of the equation are imaginary.

If the roots of the equation $x^2 - 2cx + ab = 0$ are real and unequal,then the roots of the equation $x^2 - 2(a + b)x + a^2 + b^2 + 2c^2 = 0$ are

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