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Question

Discuss the nature of the roots of the equation 4ax2+3bx+2c=0, where a,b,cR and are connected by the relation a+b+c=0.

A
All roots are imaginary.
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B
All roots are real.
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C
They can be real or imaginary depends on the value of a,b,c.
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D
None of these
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Solution

The correct option is D All roots are real.
Δ=9b232ac=9b2+32a(a+b)=9b232ab=9b2+32a2=b2+8(b2+4ab+4a2)=b2+8(b+2a)2=+ive
Roots are real

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