Chapter 4, Problem 17SGA

To determine

To find: The discriminant of $3m^2-10m+5=0$ and describe the nature of the roots of the equation. Then solve the equation by using the Quadratic Formula.

Answer to Problem 17SGA

Two real distinct roots

  $m=\frac{5\pm \sqrt{10}}{3}$

Explanation of Solution

Given information: $3m^2-10m+5=0$

Calculation:

Given:

  $3m^2-10m+5=0$

Use $b^2-4ac$ formula and check the roots

  ${\left(-10\right)}^2-4\cdot 3\cdot 5=40>0$

Two real distinct roots

Use quadratic formula

  $x=\frac{-\left(-10\right)\pm \sqrt{40}}{6}$

Solve for x

  $x=\frac{5\pm \sqrt{10}}{3}$