For what values of $b$ does the equation $x^2+bx+1=0$ have no real solutions?

All $b\lt 0$

All $b\lt 1$

All $b\lt 2$

$0\lt b \lt 4$

$-2\lt b \lt 2$

Approach

For no real solutions, the discriminant (expression under the square root of the quadratic formula) must be negative.

$$ x=\frac{-b\pm\sqrt{b^2-4ac}}{2a} $$ $$ b^2-4ac \lt 0 $$ $$ b^2-4(1)(1) \lt 0 $$ $$ b^2-4 \lt 0 $$ $$ b^2 \lt 4 $$

The appropriate way to solve this inequality would be to graph $b^2$ and check when it is below the line $y=4$. This occurs from $-2$ to $2$, noninclusive of the endpoints.