Review question

# When are the roots for $x^2-bx+c=0$ real and positive? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R5138

## Question

Consider the equation $x^2-bx+c=0,$ where $b$ and $c$ are real numbers.

1. Show that the roots of the equation are real and positive if and only if $b>0$ and $b^2\geq 4c>0$, and sketch the region of the $b$-$c$ plane in which these conditions hold.

2. Sketch the region of the $b$-$c$ plane in which the roots of the equation are real and less than $1$ in magnitude.