Chapter 4.2, Problem 7CFU

To determine

To find: The discriminant of equation $m^2+12m+36=0$ and describe the nature of the roots of the equation.

Answer to Problem 7CFU

  $m_1=m_2=-6$

Since delta is zero, the quadratic has two equal real roots

Explanation of Solution

Given information: $m^2+12m+36=0$

Calculation:

We’ll re-write the quadratic to identify its coefficients, a, b, c

  $m^2+12m+36=0$

We’ll recall the formula that gives the discriminant delta.

  $\Delta =b^2-4ac$

We’ve identified a, b, c

  $a=1;b=12;c=36$

We’ve evaluated delta that is zero.

  $\Delta ={12}^2-4\times 36=144-144=0$

We’ve computed the equal roots of the quadratic.

  $m_1=m_2=-12/2=-6$

  $m_1=m_2=-6$

Since delta is zero, the quadratic has two equal real roots.