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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

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

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
6 years ago
since roots are imaginary c2-4ab<0
since 3b2>0 the given expression3b2x2 + 6bcx + 2c2 has minimum value.
\frac{4(3b^{2}*2c^{2})-36b^{2}c^{2}}{4(3b^{2})}= -c^{2}>-4ab
Thanks and Regards
Shaik Aasif
askIITians Faculty

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