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Question

If $$a, b\in R, a\neq 0$$ and the quadratic equation $$ax^2-bx+1=0$$ has imaginary roots, then $$(a+b+1)$$


A
is positive
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B
is negative
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C
is zero
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D
depends on the value of b
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Solution

The correct option is A is positive
The quadratic equation $$ax^2-bx +1 =0 $$ has imaginary roots.
Hence, the expression $$ax^2-bx+1 $$ is either positive for all values of $$x$$ or negative for all values of $$x$$. 
When $$x=0$$,  $$ax^2 -bx+1 = 1 >0$$
Hence, $$ax^2-bx+1 >0 $$ for all values of $$x$$
When $$x=-1$$ ,
$$ax^2-bx+1 = a+b+1 >0$$
Hence, option A is correct.

Mathematics

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