Question

If $b\in F^{\prime }$ then the roots of the equation $(2+b)x^2+(3+b)x+(4+b)=0$ is

• A. real and imaginary
• B. real and equal
• C. imagenary
• D. cannot predicted

Answer 1

The correct option is C imagenary

$(2+b)x^2+(3+b)x+(4+b)=0$

$D=(3+b{)}^2-4(2+b\left)\right(4+b)=b^2+6b+9-4b^2-24b-32=-3b^2-18b-23=-3(b^2+6b+9)+4$

$=-3(b+3{)}^2+9<0$

So roots are imaginary