Question

use the discriminate to determine the number and type of solution of the following quadratic equation x^2-12x+36=0

Answer 1

Number of solution is 1

Type of solution is REAL SOLUTION

Explanations

Given the quadratic equation expressed as:

`x^2-12x+36=0`

The formula for the discriminant is expressed as:

`D=b^2-4ac`

where

a = 1

b = -12

c = 36

Substitute

`\begin{gathered} D=(-12)^2-4(1)(36) \\ D=144-144 \\ D=0 \end{gathered}`

Since the discriminant is equal to zero, hence the quadratic equation will have one real solution.

Note that the nature of the solutions for discriminant greater than zero is 2 real roots while it is complex for a discriminant less than zero.