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Question

If the roots of the equation ax2+2bx+c=0 imaginary, then the roots of the equation ax2+2(a+b)x+(a+2b+c)=0 will be:

A
Imaginary
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B
Real
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C
Rational
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D
Irrational
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Solution

The correct option is A Imaginary
ax2+bx+c=0
For imaginary roots, D<0
(2b)24ac<0
b2ac<0-Equation 1.

Since, ax2+2(a+b)x+(a2b+c)
D(2(a+b)2)4(a+2b+c)(a)
4(a2+b2+2ab)4(a2+2ab+ac)
4(b2ac)<0
Here D<0 imaginary roots.



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