Chapter 12.6, Problem 2ST

To determine

To find: the value of an algebraic equation as mentioned in the problem.

Answer to Problem 2ST

The value of $2x^2+6x+3$ is $x=-0.6335,-2.366$ .

Explanation of Solution

Given information:

The equation mentioned is $2x^2+6x+3=0$ .

Formula:

The quadratic equation formula $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ where $a,b,c$ is any constant.

Calculation:

Consider an algebraic equation as $2x^2+6x+3$ .

The mentioned equation is in the form of $a{x}^2+bx+c=0$ where $a=2,b=6,c=3$ .

Recall that quadratic equation formula $\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ where $a,b,c$ is any constant.

Therefore

  $\begin{array}{l}2x^2+6x+3\Rightarrow x=\frac{-6\pm \sqrt{6^2-4*2*3}}{2*2}\Rightarrow x=\frac{-6\pm \sqrt{36-24}}{4}\Rightarrow x=\frac{-6\pm \sqrt{12}}{4}\\ \Rightarrow x=\frac{-6\pm 2\sqrt{3}}{4}\Rightarrow x=\frac{-3\pm \sqrt{3}}{2}\Rightarrow x=\frac{-3+\sqrt{3}}{2},\frac{-3-\sqrt{3}}{2}\Rightarrow x=-0.6335,-\mathrm{2.366.}\end{array}$

Therefore the value of $2x^2+6x+3$ is $x=-0.6335,-2.366$ .