Chapter 7.3, Problem 6WE

To determine

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

Answer to Problem 6WE

As the discriminant is negative so the roots will be imaginary conjugates.

Explanation of Solution

Given information :

Given equation $5t^2-4t+3=0$

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,

  $\begin{array}{c}D={\left(-4\right)}^2-4\left(5\right)\left(3\right)\\ =16-60\\ =-44\end{array}$

As the discriminant is negative so the roots will be imaginary conjugates.