Chapter 7.3, Problem 1WE

To determine

Without solving each equation, to determine the nature of roots.

Answer to Problem 1WE

The roots are real and unequal.

Explanation of Solution

Given information :

Given equation $x^2+3x-9=0$

Discriminant of the equation $a{x}^2+bx+c$ is given by the formula $D=b^2-4ac$

Discriminant of the equation also helps us to understand the nature of the roots of the equation.

In the given equation we compare it with $a{x}^2+bx+c$ and put the values in discriminant formula we get,

  $\begin{array}{c}D={\left(3\right)}^2-4\left(1\right)\left(-9\right)\\ =9+36\\ =45\end{array}$

As the discriminant is positive the roots are real and unequal.