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Which of the following is true? A: If the sum of cube of three numbers is thrice the product of the three numbers, then the sum of three numbers will be non-zero. B: For quadratic equation ax2 + bx + c = 0, If b2 < 4ac, then the given equation has only one real root. C: In the equation, x2 – (a + b)x + ab = 0, the roots of this equation will be ‘a’, ‘b’.

Which of the following is true? A: If the sum of cube of three numbers is thrice the product of the three numbers, then the sum of three numbers will be non-zero. B: For quadratic equation ax2 + bx + c = 0, If b2 < 4ac, then the given equation has only one real root. C: In the equation, x2 – (a + b)x + ab = 0, the roots of this equation will be ‘a’, ‘b’. Correct Answer Only C

FORMULA USED:

For an expression: ax2 + bx + c = 0 if b2 < 4ac, then the expression will have no real roots.

CALCULATION:

A: Let the three numbers are ‘a’, ‘b’ and ‘c’. We know that, if a3 + b3 + c3 = 3abc, then a + b + c = 0.

B: If b2 < 4ac, then the given equation ax2 + bx + c = 0 will have no real roots.

C:  x2 – (a + b)x + ab = 0

x2 – ax – bx + ab = 0

⇒ x(x – a) – b(x – a) = 0

⇒ (x – a)(x – b) = 0

⇒ x = a, b

∴, only C is TRUE.

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