Chapter 9, Problem 53SGR

To determine

To compute the discriminant of the equation and determine the number of real solutions.

Answer to Problem 53SGR

The discriminant is -4 . Since it is negative, there are no real solutions.

Explanation of Solution

Given information :

The equation is $a^2-4a+5=0$ .

Formula used :

Discriminant is found out using the formula $b^2-4ac$ , where ‘a’, ‘b’ and ‘c’ are the coefficients of the equation.

The solutions can be determined by:

If discriminant is negative, then there are no real solutions.

If discriminant is zero, then there is 1 real solution.

If discriminant is positive, then there are 2 real solutions.

Calculation :

  $a^2-4a+5=0$

Given equation.

Hence, $a=1$ , $b=-4$ and $c=5$ .

  ${\left(-4\right)}^2-4\times 1\times 5$

Putting the values in the formula.

  $=16-20$

Simplifying

  $=-4$

This is the discriminant. Since it is negative, there are no real solutions.