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Complex Numbers & Quadratic Equations Test - 6

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Complex Numbers & Quadratic Equations Test - 6
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    If the roots of the equation bx2 + cx + a = 0 be imaginary, then for all real values of x, the expression 3b2x2 + 6bcx + 2c2 is

    Solution

    As, bx2 + cx + a = 0 has imaginary roots 
    So, c2 < 4ab 
    Now, 3b2 x2 + 6bcx + 2c2 
    = 3(bx + c)2 – c2 ≥ – c2 ≥ – 4ab 
    Hence, option C is correct.

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