Chapter 4.2, Problem 25E

To determine

To find: discriminant of $2k^2+5k=9$ and describe the nature of the roots.

Answer to Problem 25E

  $x=\frac{-5+\sqrt{97}}{4}\text{ or }x=\frac{-5-\sqrt{97}}{4}$

Explanation of Solution

Given information: $2k^2+5k=9$

Calculation:

Given

  $\begin{array}{l}2k^2+5k=9\\ 2k^2+5k-9=0\end{array}$

Discriminant

  $b^2-4ac={\left(5\right)}^2-4\ast 2\left(-9\right)=25+72=97$

Nature of roots

  $b^2-4ac>0$

So the quadratic equation has two distinct real roots/zeros.

Quadratic formula

  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substitute values

  $x=\frac{-5\pm \sqrt{97}}{4}$

  $x=\frac{-5+\sqrt{97}}{4}\text{ or }x=\frac{-5-\sqrt{97}}{4}$