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

Solution

## The correct option is A is positiveThe 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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